IPENZ Transactions, Vol. 25, No. 1/CE, 1998

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Design and construction of rubble moundbreakwaters

Gavin N Palmer1, BE(Hons), PhD, MIPENZ

Colin D Christian2, BSc(Eng), CEng, PhD, MIPENZ , MICE, MASCEThe principal function of a rubble mound breakwater is to protect a coastal areafrom excessive wave action. The dissipation of wave energy through absorbtionrather than reflection distinguishes rubble mound breakwaters from other types offixed breakwater. A principal design objective is to determine the size and layoutof the components of the cross-section. Designing and constructing a stablestructure with acceptable energy absorbing characteristics continues to relyheavily on past experience and physical modelling. This paper outlines keydesign and construction issues, with particular regard to armour stability.

Keywords: breakwaters, harbour structures, revetments, riprap, rubble, shoreprotection

1Senior Environmental Engineer, City Design, PO Box 6543, Wellesley St,Auckland (formerly Postgraduate Student, Department of Civil and ResourceEngineering, University of Auckland) and 2Senior Lecturer, Department of Civiland Resource Engineering, University of Auckland, Private Bag 92-019,Auckland.

This paper, originally received on 13 June 1997, was received in revised form on12 June 1998.

1. IntroductionThe principal function of a rubble mound breakwater is to protect a coastal area from excessive waveaction. Incident wave energy is dissipated primarily through turbulent runup within and over thearmour layer (Figure 1). If the wave is steep or the seaward slope of the breakwater is relatively flatthen the wave will overturn and plunge onto the slope, dissipating further energy. Some of theremaining energy is converted to potential energy as the wave runs up the slope whilst the balance isreflected seaward and also transmitted to the leeward (sheltered) side. In most situations only limitedovertopping is tolerated and so most transmission occurs internally. Some of the internallytransmitted wave energy is dissipated during flow through the core, with the remainder appearing as awave on the leeward side. The effectiveness of a breakwater is judged by its ability to limit the heightof this transmitted wave.

The bulk of the cross-section comprises a relatively dense rockfill core. This is armoured with oneor two layers of rock or one of the numerous types of precast concrete armour unit. The outer layer isreferred to as the primary cover layer. The term “rubble” as used here includes rock, riprap andprecast concrete armour units. Similarly, “armour unit” includes both rock and precast concrete units.

The dissipation of wave energy largely through absorbtion rather than reflection distinguishesrubble mound breakwaters from other types of fixed breakwater. The famous rubble moundbreakwaters at Cherbourg and Plymouth constructed late last century apparently arose fromdifficulties dissipating wave energy through reflection (Townson 1973). Designing and constructing astable structure with acceptable energy absorbing characteristics continues to rely heavily on pastexperience and physical modelling. This paper outlines key design and construction issues, withparticular regard to armour stability. It is relevant to other coastal rubble mound structures, such asgroynes, revetments and training walls.

2. Design approachA principal design objective is to determine the size and layout of the components of the cross-section.This traditionally involves empirical formulae and other guidelines like those given by the PermanentInternational Association of Navigation Congresses (PIANC) (1980) and the United States ArmyCorps of Engineers (USACE) (1984).

IPENZ Transactions, Vol. 25, No. 1/CE, 1998

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FIGURE 1: Cross-section of a typical rubble mound breakwater.

Reviews of failures of full size structures like those presented by Bruun (1979), Baird et al. (1981),Sorensen and Jensen (1986), Silvester and Hsu (1989) and others are useful, along with theinformation presented by PIANC (1985). The latter present information on 161 breakwatersconstructed in 27 different countries.

Following preliminary design, breakwater performance, in particular armour stability, maximumrunup, wave reflection and wave transmission, is normally checked with a physical model in a waveflume. Physical models are constructed geometrically similar to the full size structure. It is assumedthat as gravitational forces dominate, models are scaled with the Froude model law. Viscous forcesare made negligible by selecting linear scales of sufficient size and by careful selection of corematerial for the model. Scale ratios usually depend on the maximum wave height and water depththat can be reproduced in the flume along with the available size of model armour units, but aretypically within the range 20 to 50.

Consideration needs to be given to environmental effects associated with visual impact, occupationof the seabed, changes in wave patterns and the mobilisation of fines during core dumping. Wavereflection and diffraction may impact on navigability, and the breakwater itself may influence currentswhich could cause scour and alter bathymetry, particularly at the advancing end during construction(Hickson and Rodolf 1951, Fried 1965, Kaplan 1971, Thorpe 1984, Van Damme et al. 1985, Sorensenand Jensen 1986). This can increase the amount of material required or affect the stability of nearbystructures.

As the bulk of a breakwater is underwater, construction and inspection is difficult, especially underrough seas. The practicalities of translating an idealised model into a full size structure should beborne in mind. Moore (1989) presents useful guidance on “constructability” in which design isplanned for construction. A design that has worked well in shallow water should only be extrapolatedto deep water if due consideration has been given to the practicalities of construction and the possiblysignificant differences in wave climate and structural behaviour. Breakwaters in deep water should bemodel tested with an appropriate sea state.

3. Design and construction issues

3.1 Sea state

Wave direction, either normally incident or oblique, refers to the direction of wave travel with respectto the breakwater axis. In comparison, length of wave crest, either long or short, is a three-dimensional phenomenon. It is imperative that model tests represent the sea state correctly,particularly for large breakwaters and when a two-dimensional wave flume is used. The cost ofrefining the design wave height through additional data collection or analysis has to be weighedagainst the cost of over or under-designing the structure.

The significant wave height, HS is often used to characterise an irregular sea and is usually definedas the average of the one-third highest waves. The USACE (1984) recommend that H1/10, defined asthe average of the ten highest waves, be used for the design of rubble mound breakwaters. Vidal et al(1995) suggest a new wave parameter in stability formulae, Hn defined as the average height of the nlargest waves in a sea state. They show that both the wave height distribution and the total number ofwaves to achieve a given damage level are taken into account with this parameter and suggest that n is

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approximately equal to 100, but recommend further research. Jensen et al (1997) suggest that H1/20

should be used for rock slopes and that n should equal 250.

When there is a paucity of wave data and there are shallow water conditions, it may be appropriateto use the maximum height depth-limited wave for design. If so, then it is important to ensure thatstorm surge, setup or future changes in bathymetry through dredging or scour do not affect thisassumption.

3.2 Wave-breakwater interaction

The wave climate along the entire length of the breakwater should be checked to see if the bathymetryconcentrates wave energy anywhere. Where appropriate the breakwater can be aligned to minimisesuch concentrations. Concentrations of wave energy can result from a change in wind directionduring a storm, with wind waves and swell arriving from different directions.

Although most energy is dissipated by the breakwater, the amount of wave reflection should bechecked to assess effects on navigation and toe scour. Large scour depths are often associated with ahigh reflection coefficient (Sawaragi 1967, Eckert 1983). A layer of rock extending seaward from thetoe can protect against scour and may cause waves to break before reaching the seaward slope,reducing the design wave height (Van Damme et al 1985).

The relationship between slope angle θ, wave height H and offshore wave length Lo can beexpressed in terms of the Surf Similarity Parameter (ξ) or Iribarren Number (Ir) given by:

21oLH

tan =

/)/(

θξ (1)

The usefulness of ξ has been demonstrated in the widely referenced work of Battjes (1975). Hegave a physical interpretation of ξ, showing that for waves that break on the slope, it is approximatelyproportional to the ratio of θ to the local steepness of the breaking wave. Resonance of uprush anddownrush with wave period occurs when ξ is within the range 2 to 3 and hence breakers are of theplunging or collapsing types (Bruun 1985).

Because of the extensive amount of data on maximum runup, Ru for smooth slopes, the use of therelationship:

u uR (rough) = r.R (smooth) (2)

is often advocated, where r is a roughness and permeability correction factor. Ru is measured relativeto the still water level (SWL), defined by the USACE (1984) as the elevation that the surface of thewater would assume if all wave action were absent. Stoa (1978) and Losada and Giménez-Curto(1981) present values of Ru for armoured slopes and show that it is not possible to associate a singlevalue of r with each type of armour. Van der Meer and Stam (1992) present empirical design formulaefor runup on smooth and rock slopes. Good results have been obtained for the numerical modelling ofwave runup on mild slopes (Christian and Palmer 1997).

3.3 Cross-section configuration

3.3.1 Slope angle

Side slopes are generally as steep as possible to minimise the volume of core material and to reducethe reach of cranes working from the crest (Moore 1989). However it may be possible to develop aless steep slope if the cranes operate from a barge. Slopes are typically within the range 1V:1.5H to1V:3H and influence the amount of interaction between armour units. As the angle increases, thecontribution to stability from friction and interlocking also increases due to the squeezing or increasein slope-parallel forces applied by adjacent units. There is however a corresponding decrease in theslope-perpendicular component of self-weight (Price 1979). This implies optimum slope angles formaximum interaction and stability (Losada and Giménez-Curto 1982).

3.3.2 Layer thickness

Armour stability generally increases with an increase in armour layer thickness. All layers should beconstructed thicker than designed to allow for settlement, provided the armour will tolerate settlement

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without breakage. Allowance should also be made for the initial settlement that occurs as the unitsnest into a more stable position under wave action.

3.3.3 Crest elevation

The elevation of the crest should be the minimum at which acceptable overtopping occurs. Thisshould be based on maximum wave runup, with an allowance for freeboard and post-constructionsettlement.

3.3.4 Equilibrium profiles

Equilibrium, S-shaped or “reshaped” profiles develop with the redistribution of material under waveaction. Extensive damage to a breakwater with a plane seaward slope usually results in such a profile,with material removed from a zone centred near the SWL being deposited at the toe. The profilecontinues to develop until equilibrium between erosion and accretion is reached. To ensureequilibrium is achieved they are usually restricted to sites with small tidal ranges. The similaritiesbetween beach step profiles and equilibrium profiles has been demonstrated by Van der Meer andPilarczyk (1987), who also present empirically derived data on the geometry of the reshaped profile.

3.3.5 Berm breakwaters

Berm breakwaters are constructed with a horizontal berm at or near the SWL, with the bermoccupying the full width of the armour layer. This is thought to give lower internal velocities than aconventional armour layer and so smaller armour, either rock or riprap, can be used. The seawardprofile retains its original overall shape, but the berm compacts under wave action into a more stableform (MacIntosh and Baird 1987). The development of the seaward profile has been physically andnumerically modelled by Van Gent (1995).

3.4 Armour layer

3.4.1 Armour type

Armour units can be classified as compact, interlocking or hollow according to their shape and meansof obtaining stability. Compact armour units which include rock and riprap use their weight, and to alesser extent friction, to resist wave action. In comparison, interlocking armour units, such as theDolos (Figure 2) rely principally on interlocking with adjacent units. A more porous armour layer iscreated enabling a higher proportion of wave energy to be dissipated within the voids between armourunits. This however tends to force the armour units apart. The breakage of several adjacentinterlocking units can lead to failure of the whole armour layer.

FIGURE 2: Dolos armour unit.

Hollow armour units such as the SHED (Shephard Hill Energy Dissipator) (Figure 3) andAccropode are placed in a regular pattern forming a single layer (Kobayashi and Kaihatsu 1995). TheAccropode was developed by Sogreah Consultants (France) in the early 1980s. The internal voidensures that satisfactory space is always available for energy dissipation, unlike compact and

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interlocking armour units where porosity is dependent on their relative positions. Like interlockingunits, hollow units are susceptible to differential settlement of the underlayer.

The USACE (1984) list some of the many types of armour unit available. They present a logicdiagram for preliminary selection which includes royalty costs and the availability of forms as criteria.Bruun (1985) presents a summary and evaluation of various armour types.

FIGURE 3: SHED armour unit.

Precast concrete armour units are used when suitable rock is unavailable or, according to thesurvey results of PIANC (1985), when HS exceeds approximately 5m. Their results also show that theygenerally weigh between 6t and 50t. The choice between rock and concrete may be influenced by adesire to blend in with existing structures or natural features.

The Tetrapod, the first of the “engineered” precast concrete armour units, was developed by theFrench company Neyrpric in 1953. This followed a film viewed by PIANC in 1949 showing the liftingof armour rock during downrush. Rather than resist this through self-weight, Neyrpric sought toimprove permeability and interlock between units (Dock and Harbour Authority 1957). Armouring ofthe extension to Wellington airport runway in 1955 was one of the earliest projects to use Tetrapods.

The Dolos (plural Dolosse) was developed in 1966 for rehabilitating the damaged breakwater atthe Port of East London, South Africa (Merrifield and Zwamborn 1967) (Figure 2). It was decided todevelop a new unit because of patents and costs of existing types. Wooden models were used to refinethe shape with the criteria of achieving high void to solid ratio and interlocking. Dolosse have beenthe subject of much research and insitu monitoring, because of the large number of failures and theneed to provide information to support ongoing management and maintenance of the many existingstructures armoured with them.

For rock it is normal to specify a tolerance on armour weight, such as 25% of the nominal weight(Van Oorschlot 1983), and a limit on the maximum percentage of armour weighing less than thenominal weight (typically 50-70%). Riprap differs from rock in that a wide range of particle sizes ispresent and the USACE (1984) recommend that it be used only where the design wave height(average of the highest 10% of all waves) is less than about 1.5m. Construction specificationsdeveloped from model testing must recognise that grading can not be checked in the field by sieving.

Careful consideration must be given to the elevation at which the primary cover layer isterminated. According to the survey of PIANC (1985) it is typically equal to 1.5HS below the SWL.Armour below this level usually consists of rock, even when concrete units are used above. Losada andGiménez-Curto (1981) present useful data on maximum rundown, the lowest elevation of the runuptip, which is not widely reported, and can be used to determine the depth of termination.

It is unusual to use different types of precast concrete armour unit within the same cover layer.Foster (1985a) describes problems interfacing Dolos and Tribar units during construction, especiallynear the SWL where most wave action is concentrated. Armour weights may vary along the length ofa breakwater in accordance with a smooth variation in water depth and hence wave height (Depuy andStickland 1976), but it may be more economic and practical to adopt a constant weight.

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Transitions are required at changes in slope, typically on the leeward side where the flatter slopenear the head is steepened to match that of the trunk (Pope and Clark 1983). Care must be taken withtransitions between new and existing armour, particularly for oblique wave attack and where the newarmour differs in weight from the existing. Baumgartner et al (1985) and Markle and Dubose (1985)describe the use of rock buttresses to support Dolos placed to rehabilitate damaged breakwaters. Forcubes there can be difficulties nesting the outer and inner layers (Groeneveld et al 1983) and also unitsin the same layer (Van Damme et al 1985).

3.4.2 Armour size and stability

It was not until 1933 that the first formula was presented, by De Castro and Briones, to aid thedesigner in selecting a rock armour weight for a given wave height. This was followed in 1938 by thesemi-theoretically derived Iribarren Formula. Model tests performed at the Waterways ExperimentStation (WES) of the USACE in the 1950s using cubes and Tetrapods showed that the inter-unitfriction coefficient, an independent variable in the formula, varied widely with armour unit shape andmethod of placement, as well as between similar tests (Hudson 1959). Further use of the IribarrenFormula at the WES was therefore abandoned, although it is still used elsewhere today. R.Y. Hudson,Chief Engineer of the WES Wave Action Section, then developed the well known Hudson formula:

θcot)1 - S(K

Hw =W 3

rD

3r (3)

where W is the dry weight of an individual armour unit in the primary cover layer, KD is an empiricalstability coefficient which is intended to account for all of the factors affecting armour stability thatare not included as variables, wr is the unit weight of the armour material, H is the design waveheight, Sr is the specific gravity of the armour unit and θ is the slope of the structure. Equation (3) isapplied to riprap by substituting the median weight, W50 for W and using the appropriate value of KD.

Hudson derived (3) by evaluating the fluid drag and inertial forces acting on an individual armourunit in the primary cover layer, and equating these to the weight of the armour unit. The frictionbetween units was ignored but its effect was assumed to be included in KD. Values of KD aredetermined from model tests by measuring the value of H at which some threshold level of damage isexceeded. Values are presented by the USACE (1984) and others and are periodically revised.

More than 20 other formulae exist, some including inter-unit friction and wave period, T asvariables (PIANC 1976). Most, including (3), are for the condition of long crested waves movingperpendicular to the axis of a straight breakwater. Losada and Giménez-Curto (1979) present design(interaction) curves based on model tests showing the relationship between H, T and θ for variousarmour types. Holtzhausen and Zwamborn (1993) present statistically derived design formulae forDolos on a 1:1.5 slope in deep water and Burcharth and Liu (1993) present design charts on thestability and strength of Dolos.

Van der Meer (1995) presents the following empirically derived formulae for sizing rock armour:

H D x S NS n/ . ( / ). .∆ 500 18 0 26 2ξ = P (4)

for plunging waves (ξ<2-4), and

H D S NS n/ . ( / ) cot. .∆ 50 1 0 0 13 0 2= −P Pαξ (5)

for surging waves, where ∆ is the relative mass density, Dn50 is the nominal armour diameter, P is adimensionless permeability factor and N is the number of waves to achieve the damage level, S givenby:

S A De n= / 502 (6)

where Ae is the cross-sectional area of erosion.

According to Van der Meer (1995), the value of P varies from a minimum of 0.1 for an armourlayer with a thickness equal to 2Dn50 on an impermeable core, to a maximum of 0.6 for ahomogeneous structure consisting only of rockfill. He recommends that a sensitivity analysis beperformed on all parameters as part of the design process.

Increasing the waist thickness of the Dolos, defined as the ratio of the width of the octagonalcentral stem (measured between flats) to the longest dimension of the unit, reduces stresses within theunit but decreases stability (Scholtz et al 1983, Zwamborn and Scholtz 1987, Burcharth and Liu

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1993). Burcharth and Brejnegaard-Nielsen (1987) report the same result, but only for damage greaterthan 5% within the zone SWL±HS. This is apparently due to less interlocking and lower armour layerporosity. The results of limited model tests comparing Accropode and Dolos are presented byHoltzhausen and Zwamborn (1991). They conclude that Accropode are more stable than Dolos forlong period waves (ξ>3), but have similar stability for shorter waves.

Users of stability formulae must ensure that their definition of “acceptable damage” is consistentwith that for which each formula and its respective empirical coefficients were derived. For exampleIribarren accepted that wave action would form the equilibrium slope angle if it was initially toosteep.

3.4.3 Definition and assessment of damage

A pre-determined, acceptable level of damage is tolerated under design conditions. Damage isgenerally defined as the removal or breakage of individual armour units, or sliding of the armour layeren-masse. For precast concrete units, rocking is classed as damage too since this can lead to breakageand progressive failure of the armour layer. For breakwaters subjected to heavy overtopping orinternal wave transmission, the stability of armour near the top of the leeward armour layer may berelevant (Walker et al 1975, Foster 1985b, Anderson et al 1993).

When using a model to determine threshold damage conditions, a small amount of damage mustbe observed which is generally referred to as the “no damage” condition. It is important to assess howdamage observed in the model will relate to performance of the full size structure and to interpretmodel results accordingly.

One approach is to express the number of units damaged as a percentage of the total number ofunits on the slope. One drawback is that the value calculated depends on the number of units in thearmour layer, making comparison of different cross sections and armour types difficult. A betterapproach is to express damage as the percentage of armour units displaced from the zone of activearmour removal (Ouellet 1973). This zone extends from the middle of the crest down the seaward sideto a depth of one characteristic wave height below the SWL. Ouellet (1973) defines the characteristicwave height as that corresponding with 1% damage. The “zero damage” or “no damage” condition istypically within the range 0-5%. For riprap slopes, including equilibrium profiles, it is moreappropriate to describe movement of a volume of material using (6) or similar.

Because precast units can break as the result of rocking, a more relevant approach is to usecombinations of rotation and displacement to classify the movement of individual units. A damagedistribution can then be determined by comparing percentage damage to damage class, wherepercentage damage is expressed in terms of the total number of units within the zone of active armourremoval. Based on the susceptibility of each type of unit to breakage, allowable damage distributionscan be used to evaluate model test results (Partenscky et al. 1987).

3.4.4 Armour unit strength

Because of the complex time-dependent loading it is difficult to accurately design a reinforcingscheme for interlocking concrete units. Disadvantages of reinforcement are the substantial increase incost and the possibility of cracking resulting from corrosion. The latter can be eliminated if syntheticreinforcing material is used.

Armour unit strength can be assessed with full scale drop tests to simulate inter-unit impacts andforces. Groeneveld et al (1983) suggest that large concrete units are more susceptible to breakage thansmall units, due to reduced reserve strength and higher temperature gradients during curing. HoweverPIANC (1985) report that their survey shows that breakage of larger precast concrete units is no morefrequent than that of smaller units.

Alternative methods of measuring stress in model units are described by Burcharth et al (1991).One approach is to observe the number of rocking and displaced units and then estimate the numberthat would break in the full size structure. A second approach is to measure forces at several locationswithin selected units which are then extrapolated elsewhere within the unit using a numerical model.A further approach is to scale the strength of the model armour unit material. This avoids subjectivedamage interpretation, but means that broken units can not be re-used.

Impact forces and the temporal and spatial distribution of acceleration have been the subject ofexperimental research by Van der Meer and Heydra (1991), Bürger et al (1993) and others.D’Angremond et al (1995) present empirical design curves for the structural design of Tetrapods,

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based on the measurement of stresses in model units. Turk and Melby (1995) present the results ofmodel tests with Dolos and conclude, amongst other things, that rocking and the associated inter unitimpact produces impact stresses that, when combined with static and wave induced stresses, can oftenbe high enough to exceed the concrete strengths typically found in full size units.

Pope and Clark (1983) and Phelp et al. (1995) describe techniques used to monitor full size Dolosarmoured breakwaters. Kendall and Melby (1993) present the results of monitoring Dolos on theCrescent City breakwater over a six year period. They conclude that static stress is the mostsignificant structural design parameter for these large (38 tonne weight, approximately 4.5 m overalllength) Dolos units and report that static stress increases over time as a result of subtle movementsand inter unit wedging. Luger et al (1995) surveyed 357 broken Dolos units on seven breakwaters andclassified each unit according to one of six breakage modes. They report that 89% of breakagesoccurred near the fluke-shank intersection and recommend incorporating a large fillet extending tomid-shank.

3.4.5 Handling and placing armour units

Rock armour should be placed with the longest dimension perpendicular to the slope. Althoughinterlocking concrete units are usually oriented randomly, the desired packing density (number ofunits per unit surface area) is ensured by specifying insitu coordinates and placing each unitindividually. Consideration should be given to the number of crane positions and hence movementsrequired when determining armour unit positions. In some cases it may be economic to use a smallernumber of larger units. This would involve less handling, with a commensurate reduction in bothconstruction time and breakage.

Placing from a barge may be more time consuming than placing from land because of loading andpositioning and the prerequisite of a suitable sea state. It may also result in a higher rate of breakageduring placement and limit the range of permissible working conditions. Despite this, breakagegenerally occurs irrespective of the particular placement method.

If an armour layer is designed assuming regular maintenance then consideration should be givenduring design to the lifting and placing equipment required and the methodology. Lifting slings andhooks may be difficult to attach to units insitu, especially underwater. Cast-insitu lifting eyes must bemaintained in good order since retrofitting is difficult.

3.4.6 Toe support

The critical sea state for toe design, and hence model tests, will usually be at low tide, provided waveheights are not depth-limited. Scour of the leeward toe can result from overtopping (Walker et al1975). A toe structure of placed armour units, often rock, provides direct support of the armour layerand also surcharges the seabed against a slip circle failure. The literature contains numerous reportson armour layer failures initiated by loss of toe support or leaching of a sandy seabed, along withrehabilitation methods (Danel and Greslou 1963, Kjelstrup and Bruun 1983, Smith and Gordon 1983,Silvester and Hsu 1984, Thorpe 1984, Read 1986, Sorensen and Jensen 1986). Exposure of the corecan result, leaving it vulnerable to wave attack. Fredsøe and Sumer (1997) describe scour mechanismsnear the head and present empirical formulae for sizing protective rock armour.

A toe structure formed from cast insitu concrete is essential with hollow units, and is why theytend to be restricted to shallow water. In some cases the stability of interlocking units is improved bymodifying the shape of a unit such as the Dolos (Van Dijk et al 1983) or by special orientation. Froma construction point of view, the latter is only practical in shallow water. If a geotextile is used,consideration must be given to the practicalities of placing it underwater. Care must also be taken toprevent it being undermined.

3.4.7 Special considerations near the head

The seaward end of a shore connected breakwater is termed the “head” and is circular in plan.Difficulties with construction in deep water and high exposure to storms need consideration, alongwith concentrations of wave energy due to diffraction. A wave trough on the leeward side coincidentwith maximum runup on the seaward side may create a head for internal flow, dislodging leewardarmour. Vidal et al. (1991) provide guidance on required armour weights at breakwater heads.

Because the head is wider than the trunk it is possible to deflect it either inwards or outwards. Thechoice should consider the effect on the redirection of wave energy, and hence navigation, harbour

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circulation patterns and sediment transport. Consideration should be given to whether or not thecompleted breakwater can be easily extended in the future.

3.5 Underlayer

The underlayer acts as a foundation for the armour layer and as a filter to prevent the core beingeroded. It also protects the core during construction. The size of rock to be used in the underlayer isexpressed as some proportion of W. This ensures adequate interlock between adjacent layers and alsothat the gradation reduces the potential for internal erosion. Armour stability generally increases withan increase in underlayer permeability.

Hedges (1984) has suggested the use of “binders” (shear keys) between the armour layer andunderlayer to prevent sliding of the former, but this is not common practice. The use of this techniqueis described by De Carvalho (1964) in which specially shaped precast concrete “cast through stones”were used to link two layers of rock armour.

3.6 Core

Core permeability affects wave runup and armour stability, with low permeability causing higherrunup and lower stability (Timco et al 1985, Van der Meer and Pilarczyk 1987). Although a densecore reduces wave transmission, a minimum of fines should be used so as to avoid internal erosion. Agraded filter prevents removal of fines from the core but does not prevent the internal redistribution ofmaterial which may cause differential settlement. The selection of core material generally usesempirical guidelines based on past experience.

Penetration into the seabed may result in greater quantities being required than estimated duringdesign. It may also lower the crest, increasing the risk of overtopping. Significant consolidation of theseabed can occur during construction (Fang 1982) but can be managed by staging construction suchthat consolidation of the seabed occurs as construction proceeds. Because the core is deposited in aloose state, shakedown and settlement occurs initially under wave action, which may damage armourunits. Earthquake or wave induced liquefaction may be relevant design considerations.

Techniques used to analyse equilibrium profiles can be used to assess the behaviour of the exposedcore during a storm. The risk of damage is usually limited by specifying the maximum length of corewhich can be left exposed at any time during construction.

3.7 Superstructure

A superstructure consisting of a concrete cap block or wave wall (crown wall) provides access formaintenance or cargo handling, and is essential when hollow units are used. It can also reduce theamount of overtopping and strengthen the crest. It is usually poured after differential settlement of thecore has reduced to an acceptable rate.

Dynamic loadings result from wave impact on the seaward face and uplift pressure on the base.The latter can be relieved with vent holes, but this requires a commitment to keep them clean. Extravertical load may also result from wave overtopping. A parapet intended to prevent overtopping maytrap waves causing additional downrush and hence loading on armour units.

Sliding is resisted by friction between the base and the underlayer or core. Difficulties arise intrying to reproduce this with physical models, especially when the relative size of the material hasbeen altered to satisfy hydraulic scaling requirements.

Jensen (1983) presents the following guidelines:

• the wave wall should not extend above the level of the seaward armour (to minimise theforces on the superstructure)

• key the cap block into the core with a heel

• extend the core up to the underside of the cap block, and

• extend the rear of the cap block past the leeward slope to direct overtopping jets of waterpast the leeward armour to fall directly on the water surface.

The material beneath the base should either have very high permeability to relieve uplift pressures,or be of very low permeability to prevent pore water entering. The former may however dislodgearmour on the leeward side. Other useful comments are made by Baird et al. (1981). Hamilton and

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Hall (1993) present results of model tests with crown (wave) walls showing that short, stabilising legsat the seaward and leeward ends of the superstructure substantially increase stability and that stabilityalso increases with decreasing wall height. Like Jensen (1983), they recommend direct placement onthe core with armour extending up the front of the wall.

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4. ConclusionsThe principal function of a rubble mound breakwater is to protect a coastal area from excessive waveaction. Despite more than six decades of applied research, design continues to be based largely onexperience and physical modelling of the proposed structure. Interaction between armour units ispoorly understood and, as a consequence, the design of armour layers remains largely empirical.Armour stability is affected by armour weight and shape, underlayer size and shape, underlayer andcore permeability, toe support and the detailing of the superstructure. Armour layer damage must beclearly defined, interpreted and reported. Model tests and empirical formulae should be applied andinterpreted with care. It is imperative that model tests represent the sea state correctly. Thepracticalities of translating an idealised scale model into a full size structure should be assessed, withdue consideration given to the construction and maintenance phases.

5. AcknowledgementsThe principal author gratefully acknowledges the support of a University Grants CommitteePostgraduate Scholarship and the Wilkins and Davies Engineering Research Scholarship whilstperforming the research described in this paper.

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7. NotationAe Cross-sectional area of erosionDn50 Nominal armour diameterH Wave heightHn Average height of the n largest wavesHS Significant wave heightIr Iribarren NumberKD Stability coefficient (Hudson Formula)Lo Offshore wavelengthN Number of wavesP Permeability factorRu Maximum runupr Roughness and permeability correction factorS Damage levelSr Specific gravity of the armour unitSWL Still water levelT Wave period

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W Dry weight of individual armour unit in the primary cover layerW50 Median weight of graded riprapwr Unit weight of armour unit material∆ Relative mass densityξ Surf Similarity Parameterθ Slope of the structure.