Part C | 30.2
672 Part C Coastal Design
their cost is generally more due to special forms, concrete mixtures, curing times, etc., for their manufacture.
Some contain steel reinforcement but most are completely made of concrete.
The Hudson formula [30.57] is often applied to determine the stable size (mass, or weight) for design
H
D n50
D .K D cot ˛/
1=3
or
M 50 D
s H
3
K D
s
w
1
Á 3
cot ˛
;
(30.28)
where
H: characteristics wave height (H s or H 1=10 )
D n50 : equivalent cube length armor unit
M 50 : medium mass of armor unit, M 50 D s D
3
n50
s : mass of density of armor units
w : mass of density of water
: .. s == w / 1
˛: slope angle
K D : Hudson stability coefficient.
The only new variable is the Hudson stability coefficient K D . The Hudson formula is popular for the
design of concrete armor units because the K D values are available for many of the common shapes as
illustrated in Table 30.6. Unfortunately, however, the
Hudson formula does not include the influence of the
wave period T, the structure permeability P, the level
of damage S, and the number of waves N z . And, unfortunately, it is not clear which wave height to apply for
design (H s or H 1=10 ) and different K D values appear in
the literature for breaking and nonbreaking waves. The
K D values in Table 30.6 come from many sources including CEM [30.1], and Reeve et al. [30.62]. Note that
all the concrete units have K D values greater than natTable 30.6 Hudson stability coefficients for nonbreaking
waves on concrete units, zero damage, nonovertopping,
structure trunk
Armor unit
Hudson stability coefficient K D
Natural rock
4 (nonbreaking waves)
Natural rock
2 (breaking waves)
Tetrapod
8
Dolos
32 (8)
Accropod
9:515
CORE-LOC
1316
Antifer (grooved)
6:0
Cube, modified
7:5
Cube
6:5
Tribar
10
XBloc
1316
Stabit
10
ural rock. Some are licensed and have trademarks for
application.
A top-down design is followed for the standard, cross-sectional breakwater shapes illustrated in
Fig. 30.11. Ten rules for design have been developed
over the years by experience and model testing in the
laboratory. These rules cover the following topics:
1. Mass (weight) of the lower layer relative to upper
layer (W lower 1=10W upper as shown in Fig. 30.11)
2. Extent of armor layer below the water surface in
deep water
3. Armor-layer thickness
4. Number of concrete units per unit structure length
(if applicable)
5. Crest width
6. Crest elevation
7. Need for filter cloth and bedding stone at the bottom
8. Toe protection
9. Design of the head relative to the structure trunk,
and
10. Materials and construction methods.
Space does not permit a full discussion and the
designer must consult the CEM [30.1] or the Rock Manual [30.3] for complete details.
All the above is for the seaside, static stability of
the breakwater shape under the design conditions. Consideration must also be given to the stability of the
armor stones on the crest and rear-side of the structure as shown in Fig. 30.11. The maximum velocity
on the rear side of the crest during a wave overtopping event (exceeded by 1% of the waves) was given
by van Gent [30.63] and is used in the stability equation for the required, stable stone size, D n50 as found
in [30.54]. Complete details can be found in the Rock
Manual [30.3, Sect. 5.2.2.11]. No partial safety factors
are presented.
When the quarry cannot produce the size of armor
stones needed and the cost of manufacturing concrete armor units is prohibitive, then a dynamically
stable (berm or reshaping or unconventional) breakwater cross-section may be employed as illustrated in
Fig. 30.14 (from Baird and Hall [30.64]). The upper
cross-section is the conventional design and the other
cross-sections show a typical berm breakwater design
using smaller rocks and a larger volume of armor for
subsequent dynamic profile development (reshaping)
during storm events. A model for the dynamic shape
can be found in Pilarczyk [30.22] as proposed by van
der Meer [30.13] (in Pilarczyk [30.22, p. 157]). A stateof-the art report on designing and constructing berm
breakwaters has been compiled in [30.7]. Many other
recent references can be found in Torum et al. [30.65,
66].
672 Part C Coastal Design
their cost is generally more due to special forms, concrete mixtures, curing times, etc., for their manufacture.
Some contain steel reinforcement but most are completely made of concrete.
The Hudson formula [30.57] is often applied to determine the stable size (mass, or weight) for design
H
D n50
D .K D cot ˛/
1=3
or
M 50 D
s H
3
K D
s
w
1
Á 3
cot ˛
;
(30.28)
where
H: characteristics wave height (H s or H 1=10 )
D n50 : equivalent cube length armor unit
M 50 : medium mass of armor unit, M 50 D s D
3
n50
s : mass of density of armor units
w : mass of density of water
: .. s == w / 1
˛: slope angle
K D : Hudson stability coefficient.
The only new variable is the Hudson stability coefficient K D . The Hudson formula is popular for the
design of concrete armor units because the K D values are available for many of the common shapes as
illustrated in Table 30.6. Unfortunately, however, the
Hudson formula does not include the influence of the
wave period T, the structure permeability P, the level
of damage S, and the number of waves N z . And, unfortunately, it is not clear which wave height to apply for
design (H s or H 1=10 ) and different K D values appear in
the literature for breaking and nonbreaking waves. The
K D values in Table 30.6 come from many sources including CEM [30.1], and Reeve et al. [30.62]. Note that
all the concrete units have K D values greater than natTable 30.6 Hudson stability coefficients for nonbreaking
waves on concrete units, zero damage, nonovertopping,
structure trunk
Armor unit
Hudson stability coefficient K D
Natural rock
4 (nonbreaking waves)
Natural rock
2 (breaking waves)
Tetrapod
8
Dolos
32 (8)
Accropod
9:515
CORE-LOC
1316
Antifer (grooved)
6:0
Cube, modified
7:5
Cube
6:5
Tribar
10
XBloc
1316
Stabit
10
ural rock. Some are licensed and have trademarks for
application.
A top-down design is followed for the standard, cross-sectional breakwater shapes illustrated in
Fig. 30.11. Ten rules for design have been developed
over the years by experience and model testing in the
laboratory. These rules cover the following topics:
1. Mass (weight) of the lower layer relative to upper
layer (W lower 1=10W upper as shown in Fig. 30.11)
2. Extent of armor layer below the water surface in
deep water
3. Armor-layer thickness
4. Number of concrete units per unit structure length
(if applicable)
5. Crest width
6. Crest elevation
7. Need for filter cloth and bedding stone at the bottom
8. Toe protection
9. Design of the head relative to the structure trunk,
and
10. Materials and construction methods.
Space does not permit a full discussion and the
designer must consult the CEM [30.1] or the Rock Manual [30.3] for complete details.
All the above is for the seaside, static stability of
the breakwater shape under the design conditions. Consideration must also be given to the stability of the
armor stones on the crest and rear-side of the structure as shown in Fig. 30.11. The maximum velocity
on the rear side of the crest during a wave overtopping event (exceeded by 1% of the waves) was given
by van Gent [30.63] and is used in the stability equation for the required, stable stone size, D n50 as found
in [30.54]. Complete details can be found in the Rock
Manual [30.3, Sect. 5.2.2.11]. No partial safety factors
are presented.
When the quarry cannot produce the size of armor
stones needed and the cost of manufacturing concrete armor units is prohibitive, then a dynamically
stable (berm or reshaping or unconventional) breakwater cross-section may be employed as illustrated in
Fig. 30.14 (from Baird and Hall [30.64]). The upper
cross-section is the conventional design and the other
cross-sections show a typical berm breakwater design
using smaller rocks and a larger volume of armor for
subsequent dynamic profile development (reshaping)
during storm events. A model for the dynamic shape
can be found in Pilarczyk [30.22] as proposed by van
der Meer [30.13] (in Pilarczyk [30.22, p. 157]). A stateof-the art report on designing and constructing berm
breakwaters has been compiled in [30.7]. Many other
recent references can be found in Torum et al. [30.65,
66].