This page provides a summary of design information for the use of AJs in
wave applications. More detailed information and reports are provided at
AJs Documents. Several utilities
that help make common computations associated with the use of AJs are
provided at
Tools. A variety of general
coastal engineering reference material is provided at
Coastal Info.
1.0 GEOMETRY
1.1 Volume
1.2 Layer Thickness
2.0 AJs PLACEMENT
2.1 Uniform Placement
2.2 Bundle Placement
2.3 Random Placement
2.4 Coverage
3.0 HYDRAULICS STABILITY IN WAVES
3.1 Model Studies
3.2 Stability
3.3 Underlayer
AJs have six arms radiating from a central hub. The hub provides strength at
the base of the arms and also defines the maximum packing among adjacent units.

AJ armour unit. 
The geometry is defined primarily by three lengths; the length of the
unit L, the thickness of the arms T, and the length of
the fillets F. Other dimensions are the radius of the rounded
corners on the ends of the arms Ra, radius between the fillet and
the arm Rf, and the radius on the corner of th fillet, Rc.

AJs geometry definitions. 
The volume of an AJs is related to the fillet ratio,
waist ratio, and length. For standard coastal AJs with a waist ratio of r =
1 / 5.2, the relationship between volume and length is
V = a C^{3} = 0.1109 C^{3}
in which a is the volume coefficient. This
relationship is for square end AJs . In some coastal applications and in
many river applications, round end AJs are used. This is an architectural
choice made by the specifying engineer to give the structure a
"softer" look. For larger coastal applications, square end AJs
are recommended.
Small AJs are typically defined by their length, while
larger AJs are defined by their mass or weight. The table below summarizes AJs
length, volume, and mass for a range of sizes for a concrete density of γ_{cc}
= 2,400 kg/m^{3}. This table is for a waist ratio of r = 1 / 5.2
which gives a volume coefficient a = 0.1109.
AJs weight, volume, and length.

Weight (tonnes)  Volume (m^{3})  Length (m) 
1.0  0.42  1.55 
1.5  0.63  1.78 
2.0  0.83  1.96 
3.0  1.25  2.24 
4.0  1.67  2.47 
5.0  2.08  2.66 
10.0  4.17  3.35 
15.0  6.25  3.83 
20.0  8.33  4.22 
When AJs are placed with 3 legs on the underlayer
(bundle and uniform placement), the height of the AJs layer normal to the
slope is h = 0.73C for r = 1/ 5.2. In random placement,
the layer thickness is approximately h = 0.8C.
The geometry of the AJs armour unit allows it to be applied
on the slope in several configurations; uniform, bundle, and random. In all
cases, AJs are applied as a single layer armour system.
In uniform placement, the units are placed in a pattern that forms an interlocking
matrix with high porosity. Stability coefficients are very high because uniform
placement forms a matrix in which each individual armour unit is interlocked
with its neighbors. Placement rates are higher because the units are tightly
arranged on the slope. It may not be possible to use uniform placement of
AJs underwater when visibility or placement precision is restricted.

Uniform placement of AJs. 
Uniform placement of AJs requires that: 1) Three legs are
in contact with the underlayer, 2) One of the three legs points approximately
downslope, and 3) The star leg of the AJs points up and to the left if the
build direction is to the left and to the right if the build direction is to
the left. Each row of units along the face of the slope is 50% offset from the
row below it. When placing units, this results in a staggered pattern for the
AJs. The downslope leg of the unit is positioned into the gap between the
two units in the row below it. The leading edge of the installation is at a 45
degree angle across the face of the slope. Figure 3.1 shows a uniform placement
installation. The offset and 45 degree angle can be seen in the installation.
Installation starts at the toe and proceeds by adding one or
more units to each row up the slope along the 45 degree angle. This is then
repeated starting back at the toe. Special care is required in placing the toe
units to establish the proper alignment for the upslope placement. Once the toe
rows are placed, the upslope units are simply a repetition of the spacing of
the row below.
Bundle Placement is when four or more AJs are assembled in a uniform
pattern on the shore, banded together, and placed on the slope using a lifting
frame. This is an efficient means of placing units on the slope. When the
bundles are laid closely together, the stability approaches that of uniform
placement. Bundles can be placed underwater and provide a means of addressing
toe stability. The maximum bundle size depends upon the capacity of equipment
used on the project.

Bundle placement of AJs. 
There is the option to release the binding on bundles which
allows the units in the bundle to relax and slightly spread on the slope. Relaxed bundles have the benefits of bundles;
assembly onshore, four or more units place per lift, and dense unit placement
on the slope; but the stability is not dependant upon the integrity of the
binding.
AJs may be installed one unit at a time in a random placement
configuration. This is the common installation approach for most other armour
units. Maintaining
the appropriate placement density and slope coverage requires special
attention. Gaps in the coverage are not allowed. For large units, deep water,
or poor visibility, a grid specifying the location of each unit may be defined.
Crane position or RTKGPS coordinates are defined for each pick.

Random placement of AJs 
The area covered by one AJ when nested on a slope is
A = K_{p} C^{2}
where C is the AJs length and K_{p} is the
coverage coefficient or packing coefficient.
AJs coverage coefficients (r = 1 / 5.2). 
Placement  K_{p} 
Random  0.46 
Bundle  0.38 
Uniform  0.34 
where K_{p} is the packing coefficient or
area coverage coefficient. Table 3.1 summarizes coverage for AJs with a
waist ratio of 5.2. Another common definition for packing density is the number
of inplace units required to cover an area equal to C^{2}. This
is simply the reciprocal of K_{p}, so in random placement, the
value is 2.17. Some armour units define the characteristic length of the unit C,
by the width rather than length, so the number of units per C^{2}
value is not directly comparable among different units.
The table below summarizes coverage rates for a range of AJs
sizes and placement methods. Comparing bundle versus random placement there is
a tradeoff between the increased cost of the additional units on the slope
(because the units are more densely packed in bundle placement than random) and
the reduced cost of placing them as four or more units at one time. Also, since
bundle placement is more stable than random placement, smaller units may be
used. The most economical alternative depends upon the relative costs of labor,
materials, and equipment.
AJs coverage rates (r = 1 / 5.2, γ_{cc} = 2,400 kg/m^{3}).

 Random Placement  Bundle Placement  Uniform Placement 
Weight (tonnes)  Number per 100 m^{2}  Concrete per 100 m^{2} (tonnes)  Number per 100 m^{2}  Concrete per 100 m^{2} (tonnes)  Number per 100 m^{2}  Concrete per 100 m^{2} (tonnes) 
1.0  90.0  90.0  108.9  108.9  121.7  121.7 
1.5  68.7  103.0  83.1  124.7  92.9  139.3 
2.0  56.7  113.4  68.6  137.2  76.7  153.4 
3.0  43.3  129.8  52.4  157.1  58.5  175.6 
4.0  35.7  142.8  43.2  172.9  48.3  193.2 
5.0  30.8  153.9  37.2  186.2  41.6  208.2 
10.0  19.4  193.8  23.5  234.7  26.2  262.3 
15.0  14.8  221.9  17.9  268.6  20.0  300.2 
20.0  12.2  244.2  14.8  295.6  16.5  330.4 
AJs achieve high hydraulic stability though self weight
and interaction with adjacent units. The geometry of the AJs provides for a
high degree of interlocking among units with they are nested. The inplace
AJs matrix has a high porosity which allows for dissipation of wave energy.
The porosity for uniformly placed units with r = 1/5.2 is 57% and for
randomly placed is 68%. The combination of nesting with adjacent units and
dissipation of wave energy provide for very high stability coefficients.
AJs have been extensively tested in 2D wave flumes and 3D
model basins in Australia, Indonesia, and the United States. These studies have
the examined influence of wave conditions, structure slope, placement method,
packing coefficient, and waist ratio on hydraulic stability. The photographs and
stability results below are from flume tests conducted at the Manly Hydraulics Lab
in Australia. The tests were conducted using irregular waves on a slope of 1.5H:1V.
This Manly report and other lab reports are avaiable in
CoastalApplications/AJs Documents
. Results from the Manly tests for stability
are consistent with results from other tests.
 
Manly test results after 1000 waves for random placement.  Manly test results after 1000 waves for bundle placement. 
The stability coefficient is determined from the measured
conditions corresponding to the maximum waves at which the AJs were stable.
The Hudson equation is
_{}
in which W is the weight of an AJ (or bundle), H_{S}
is the significant wave height, m is the slope defined as mH:1V, γ_{cc}
is the weight density of the concrete, γ_{cw} is the weight
density of sea water, and K_{D} is the Hudson stability
coefficient. The value for K_{D} is adjusted to account for
similitude between the flume and prototype water and concrete densities. An
alternative expression for stability is the stability number N_{S}
defined as
_{}
in which D_{n} is the nominal diameter.
Experimental and design values for the Hudson stability coefficient for locations
on the structure are summarized below.
AJs Hudson stability coefficients from Manly tests (r = 1 / 5.2, m = 1V:1.5H). 
Placement  K_{D} Experimental  K_{D} Design  N_{s} Design

Random  29  16  2.9 
Bundle ^{(1)}  27  20  3.1 
Bundle Relaxed  65  20  3.1 
Uniform ^{(2)}  100+  25  3.3 
(1) Weight was defined as the weight of 4 AJs
in the bundle. Using the weight of a single AJ
gives K_{D}= 108.
(2) Uniform placement tests were not conducted during
this set of Manly tests. Experimental value for K_{D}
is from tests conducted at Oregon State University.

Lower design values for the stability coefficient are used on the head
of the structure. The recommended values for random, bundle, and uniform
placement on the head are K_{D} = 13, 16 and 20.
AJs sizes for a range of wave heights are shown in the table below
using the Hudson equation on the trunk of the structure and γ_{cc} = 2.4 t/m^{3},
r = 1/ 5.2, m = 1.5H:1V.
Recommended AJs sizes using Hudson Equation (γ_{cc} = 2.4 t/m^{3},r
= 1/ 5.2,m = 1.5H:1V).

 Random  Bundle  Uniform 
H (m)  W (t)  V (m^{3})  C (m)  W (t)  V (m^{3})  C (m)  W (t)  V (m^{3})  C (m) 
1  0.04  0.02  0.54  0.03  0.01  0.50  0.03  0.01  0.46 
2  0.33  0.14  1.08  0.27  0.11  1.00  0.21  0.09  0.93 
3  1.12  0.47  1.61  0.89  0.37  1.50  0.72  0.30  1.39 
4  2.65  1.10  2.15  2.12  0.88  2.00  1.70  0.71  1.85 
5  5.18  2.16  2.69  4.14  1.73  2.50  3.31  1.38  2.32 
6  8.95  3.73  3.23  7.16  2.98  3.00  5.73  2.39  2.78 
7  14.21  5.92  3.76  11.37  4.74  3.49  9.09  3.79  3.24 
8  21.21  8.84  4.30  16.97  7.07  3.99  13.57  5.66  3.71 
9  30.20  12.58  4.84  24.16  10.07  4.49  19.33  8.05  4.17 
10  41.43  17.26  5.38  33.14  13.81  4.99  26.51  11.05  4.63 
For bundle and uniform placement, the weight of the
underlayer stone is W_{ul} = W/10 where W the
weight of the AJs. For random placement larger underlayer stones are used
with a weight of W_{ul} = W/7. Larger stones are used
for the random placement because the voids in the armour matrix are larger. Smaller
stones for bundle and uniform provide a smoother surface which facilitates
uniform placement.
The nominal diameter, D_{n ul} of the
underlayer is defined as
D_{n ul} = (W_{ul}
/γ_{rr})^{1/3}
where γ_{rr} is the weight density of
the underlayer stone. For AJs with r = 1/5.2, underlayer weights of W/10
and W/7 approximately correspond to stones with nominal diameters that
are 1.11T and 1.25T where T is the thickness of the
AJs arm.
The allowable variation of the underlayer weight is 0.75 W_{ul}
to 1.25 W_{ul} with about 50% of the stones weighing more than W_{ul}.
The underlayer thickness corresponds to a two stone thick
layer. This is approximately two stone diameters. The underlayer thickness
should not be less than 0.3 m.
The underlayer elevation should not have deviations
exceeding 50% of the underlayer nominal diameter from the design profile.