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Coastal Applications

Design Information

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.

    1.1 Volume
    1.2 Layer Thickness

    2.1 Uniform Placement
    2.2 Bundle Placement
    2.3 Random Placement
    2.4 Coverage

    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.

Photo of AJs armour unit.
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 sketch.
AJs geometry definitions.

1.1 Volume

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 C3 = 0.1109 C3

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 γcc = 2,400 kg/m3. 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.

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

1.2 Layer Thickness

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.

2.1 Uniform Placement

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.

Photo of uniform placement.
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.

2.2 Bundle Placement

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 photo
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.

2.3 Random Placement

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 RTK-GPS coordinates are defined for each pick.

Random placement photo
Random placement of AJs

2.4 Coverage

The area covered by one AJ when nested on a slope is

A = Kp C2

where C is the AJs length and Kp is the coverage coefficient or packing coefficient.

AJs coverage coefficients
(r = 1 / 5.2).

where Kp 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 in-place units required to cover an area equal to C2. This is simply the reciprocal of Kp, 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 C2 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 trade-off 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, γcc = 2,400 kg/m3).
Random PlacementBundle PlacementUniform Placement
  per 100 m2
  per 100 m2  
  per 100 m2
  per 100 m2  
  per 100 m2
  per 100 m2  


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 in-place 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.

3.1 Model Studies

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.

Random placement test photoUniform placement test photo
Manly test results after 1000 waves for random placement.Manly test results after 1000 waves for bundle placement.

3.2 Stability

The stability coefficient is determined from the measured conditions corresponding to the maximum waves at which the AJs were stable. The Hudson equation is

  Hudson equation

in which W is the weight of an AJ (or bundle), HS is the significant wave height, m is the slope defined as mH:1V, γcc is the weight density of the concrete, γcw is the weight density of sea water, and KD is the Hudson stability coefficient. The value for KD is adjusted to account for similitude between the flume and prototype water and concrete densities. An alternative expression for stability is the stability number NS defined as

Stability number equation

in which Dn 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).

Bundle (1)27203.1
Bundle Relaxed65203.1
Uniform (2)100+253.3

(1) Weight was defined as the weight of 4 AJs
in the bundle. Using the weight of a single AJ
gives KD= 108.

(2) Uniform placement tests were not conducted during
this set of Manly tests. Experimental value for KD
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 KD = 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 γcc = 2.4 t/m3, r = 1/ 5.2, m = 1.5H:1V.

Recommended AJs sizes using Hudson Equation
(γcc = 2.4 t/m3,r = 1/ 5.2,m = 1.5H:1V).
H (m)W (t)V (m3)C (m)W (t)V (m3)C (m)W (t)V (m3)C (m)

3.3 Underlayer

For bundle and uniform placement, the weight of the underlayer stone is Wul = W/10 where W the weight of the AJs. For random placement larger underlayer stones are used with a weight of Wul =  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, Dn ul of the underlayer is defined as

Dn ul = (Wul /γrr)1/3

where γrr 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 Wul to 1.25 Wul with about 50% of the stones weighing more than Wul.

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.