The requirement of any port, harbour or marina is sheltered area, free from the sea waves. In the coastal areas where natural protection from waves is not available, the development of harbour requires an artificial protection for the creation of calm areas. For harbours, where perfect tranquillity conditions are required, large structures such as rubble mound breakwaters or vertical wall breakwaters are used. Most of the huge breakwaters are used to create favourable conditions in the lagoon and the entrance channel of ports, for manoeuvring of ships and loading and unloading of cargo and embarking and disembarking of passengers. They sometimes serve as berthing structures also but the main function of a breakwater is to reduce the energy of water waves by inducing wave breaking. Sometimes breakwaters are used to prevent silting of harbour basin and entrance channels and beach erosion. The wave action on a breakwater is reduced through a combination of reflection and dissipation of incoming wave energy.
The selection of the type of breakwater will be primarily based on the function of the breakwater, wave climate of that area, depth of water, availability of construction materials and local labour, geotechnical characteristics of sea bed, environmental concerns, aesthetics and available contractor potential. Although there are developments in construction technology, the rubble mound structures remain the most commonly used among all types of breakwaters. Rubble mound types consist of one or two layers of armour stone, one or two filter layers and a core of quarry run.
The design of rubble mound breakwater section, which is normally of a trapezoidal shape, is described in great details in the Coastal Engineering Manual (CEM, 2006). The design involves the use of Hudson equation or Vander Meer equation, usually supported by physical model studies. The conventional breakwaters are designed in such a way that no damage or only little damage is allowed on the structure. This criterion necessitates the use of large and heavy rock or artificial concrete units for armouring.
Rubble mound breakwaters have for more than a century, been used to protect the harbour basin against the violent forces of the surrounding sea. No problems aroused since these were used in relatively shallow water wave condition only. However, the need for bigger ships and harbours resulted in construction of breakwaters in deep water. This development resulted in the failure of several large rubble mound breakwaters as procurement of large heavy rocks was difficult. Since then different types of breakwaters were developed to suit marine conditions, and berm breakwater is the result of one such research in which smaller rocks could be used.
Berm breakwater is a three sloped structure with the middle slope being horizontal called as 'berm' (Fig. 1.1). Due to wave attack the seaward profile reshapes and forms a stable profile which can withstand even higher waves. The final profile after reshaping will be in the form of S- shape (Priest et al., 1964). Many coastal engineers have proved that S- shaped breakwaters are more stable than conventional breakwaters under certain conditions. In S- shaped breakwaters, the breaking wave usually does not strike the exposed breakwater slope, but plunges into the gentle horizontal part of the breakwater and dissipate their energy over a large area within the berm. This concept allows the designer not only to reduce the armour stone weight, but also to use a wide range of armour stones.
Fig. 1.1 Cross section of Berm breakwater
The breakwaters are normally constructed using natural stones or concrete blocks as primary armour units. Fig. 1.2 shows some of the artificial armour units (concrete units) developed over the years.
Fig. 1.2 Examples of Artificial Armour Units (Ref: Pilarczyk and Zeidler, 1996)
Breakwaters are the structures constructed to "break the waves". They are designed to reduce the effect of wave to acceptable levels to create a protected lagoon area (Harbour). An optimum breakwater from its hydraulic performance point of view should transmit and reflect wave energy as low as possible and dissipate the energy as high as possible. Various types of breakwaters are in use throughout the world. Research activities are in progress to study the performance characteristics of different types of breakwaters in order to recommend the feasible one for the prevailing environment.
2.2 Classification of breakwaters
Breakwaters are classified mainly as:
Rubble mound or heap breakwaters,
Upright or vertical wall breakwaters,
Mound with superstructure or composite breakwaters,
Special type of breakwaters.
2.2.1 Rubble mound breakwaters
These are trapezoidal shaped breakwaters and the oldest form of coastal protection work. A rubble mound breakwater dissipates the major part of the incoming wave energy by inducing wave breaking on the slope and partly by porous flow in the mound. The remaining energy is partly reflected back to the sea and partly transmitted into the harbour area by wave penetration and wave overtopping (if the breakwater is low crested). Various kinds of rubble mound breakwaters have been constructed depending on the purpose of the breakwater (Fig. 2.1).
Fig. 2.1 Types of rubble mound breakwaters (Ref: Lykke Andersen, 2006)
The most simple breakwater consist only of a mound of stones called as rubble mound breakwater (Fig. 2.1-a). However, this type of structure is very permeable, and may cause significant wave and sediment penetration. In addition, large stones are expensive, because most quarries generate a lot of finer material and a relatively small number of large stones. Fig. 2.1-b and 2.1-c are the two most common types of rubble mound breakwaters known as conventional rubble mound breakwaters with and without a superstructure respectively. These consist of various layers with primary layer exposed to wave action. The primary armour layer consists of rock or concrete units which are large and heavy to remain in their position during wave conditions. This layer also protects the bottom layers namely secondary layer and core. The secondary layer prevents finer material being washed out through the primary armour layer acts as filter layer. The core consists of fine material which acts as barrier for the water to pass through it. A superstructure is provided when overtopping is not to be allowed.
Since the 1980s a design based on natural reshaping of the front rock armour during wave action has gained more attention (Fig. 2.1-d) (Lykke Andersen, 2006). This type of breakwater is known as berm breakwaters or reshaping breakwaters. The main advantage of this structure is that simpler construction methods can be applied. The berm breakwater concept is described in detail in later sections.
Lately, non-reshaping berm breakwaters have been considered, often with several stone classes to maximize the total stability and quarry utilization, as indicated in Fig. 2.1-e. Especially in Iceland this structure is widely used, and is therefore also known as the Icelandic type of berm breakwater. Structures constructed with an S-shaped profile (Fig. 2.1-f) are typically used in large water depths to reduce the volume of material, but construction costs are in most cases significantly larger than for the reshaping berm breakwater, resulting in approximately the same profile. Fig. 2.1-g shows a reef breakwater which is a submerged breakwater mainly used for protecting beaches.
2.2.2 Upright or vertical wall breakwaters
Vertical or upright wall breakwaters (Fig. 2.2) are of huge concrete blocks, gravity walls, concrete caissons, rock filled timber cribs and concrete or steel sheet pile walls. The selection of type of breakwater would be primarily based on the wave climate in that area, depth of water, availability of construction materials and local manpower, geotechnical nature of seabed, function of breakwater, technical know-how and contractor potential available.
Fig. 2.2 Vertical wall breakwater (Ref: Takahashi, 1996)
2.2.3 Mound with superstructure or composite breakwaters
Composite breakwaters are combination of rubble mound and vertical wall. These are used in locations where either the depth of water is large or there is a large tidal range and in such situations, the quantity of rubble stone required to construct a breakwater to the full height would be too large. In such conditions, a composite breakwater is constructed which is a structure with rubble mound base and a super structure of vertical wall as shown in Fig 2.3.
Fig. 2.3 Composite breakwater (Ref: Takahashi, 1996)
2.2.4 Special type of breakwaters
Special type breakwaters are those employing some kind of special features and are not commonly used. Special type breakwaters can be divided into two kinds. One is the non gravity type breakwaters such as a pile type, floating, pneumatic etc. The other is the conventional breakwater with special features conceived to improve the function and stability of breakwater. Fig. 2.4 shows some of the special types of breakwaters. Some special breakwaters are as follows;
Curtain wall breakwater - commonly used as secondary breakwater to protect small craft harbours.
Sheet pile walls - used to break relatively small waves.
Horizontal plate breakwater - can reflect and break waves and are supported by a steel jacket.
Floating breakwater - very useful as breakwater in deep waters especially in places where the ground soil is poor for foundation.
2.2.5 Classification of Breakwaters Based on Stability Number (Ns)
Vander Meer (1988) classified the breakwaters based on the "Wave height parameter" or "Stability number", Ns i.e. H/Î”D parameter as:
â€¢ Caissons or Seawalls (H/Î”D < 1): No damage is allowed for these fixed structures. The diameter D can be the height or Width of the structure.
â€¢ Stable breakwaters (H/Î”D = 1 - 4): Generally uniform sloped structures with little damage (displacement) allowed under severe design conditions. The diameter D is the characteristic diameter of the unit, such as the nominal diameter.
Fig. 2.4 Special breakwaters (Ref: Takahashi, 1996)
â€¢ S -Shaped and Berm breakwaters (H/Î”D = 2 - 6): More or less steep slopes above and below the still water level with a more gentle intermediate part termed as a berm are the characteristics of these structures. This intermediate part reduces the wave forces on the armour units.
â€¢ Rock slopes / Beaches (H/Î”D = 6 - 20): The diameter of the rock is relatively small. The structure cannot withstand severe wave attack without displacement of material. The profiles which are being developed under different wave boundary conditions become the design objective.
2.3 Berm breakwaters
As explained earlier, berm breakwater is a type of rubble mound breakwater with a horizontal berm at or around Still Water Level (SWL). This berm is allowed to reshape by the waves into a stable profile. The advantage of this breakwater is that, lighter weight of the armour stones are required than for the conventional rubble mound breakwater and may thus be economical. This is especially true if it is necessary to use concrete cover blocks on the conventional rubble mound breakwater when large natural armour stones may not be available. Their natural responses to hydrodynamic loads make them economically attractive because, rock of lesser weight can be used in these types of breakwaters. The movement of material which results in sorting and nesting maximizes the inter-particle interlocking and the subsequent reforming of the profile that increases the stability of this structure (Van Gent, 1993). The berm breakwater is designed to optimize the utilization of the quarry material for the available construction equipment. Berm breakwater performs better than the conventional structures when exposed to waves exceeding design conditions.
The berm breakwater concept is relevant to many hot climate port locations where only relative small size rocks are available due to rock degradation. In many of these cases the necessary armour stone weight on a conventional two layer rubble mound breakwater is so large that concrete armour blocks are required or the slope has to be very flat. In these cases the berm breakwater is a good alternative. It is clear that even a non-reshaped berm breakwater requires cover stones with less weight than required for a conventional rubble mound breakwater due to the voluminous permeable berm. In many cases the total construction and repair costs are significantly lower for a berm breakwater compared to a conventional rubble mound breakwater, especially in hot climate locations and in large water depths (Lykke Andersen, 2006).
Due to the large porosity in the berm, the structure is very stable as most of the energy gets dissipated near the berm. A berm breakwater is considered to be a very tough structure as it is very difficult to destroy, even a dynamically stable berm breakwater, by incoming head-on-waves, unless the structure is overtopped or the berm is too narrow. A conventional rubble mound breakwater is more brittle and repair operations more difficult.
Wave energy on berm breakwater is dissipated by wave breaking over the berm and by porous flow in the mound. The flat slope around the water level and a highly energy absorbing porous medium give little reflection from a berm breakwater, thus better manoeuvring conditions in front of the entrance and less scour in front of the structure. Further run-up and overtopping are generally smaller than for a conventional straight and steeper breakwater slope.
Berm breakwaters can be classified based on its reshaping as:
Statically Stable Non- Reshaped: In this condition few stones are allowed to move, similar to the condition for a conventional rubble mound breakwater. The H/ï„D value is less than 1.5 for a statically non-reshaped breakwater (PIANC MarCom, 2003).
Statically Stable Reshaped: In this condition the profile is allowed to reshape into a profile, which is stable and where the individual stones are also stable. The H/ï„D value ranges from 1.5-2.7 for a statically reshaped berm breakwater (PIANC MarCom, 2003).
Dynamically Stable Reshaped: In this condition, the profile is reshaped into a stable profile, but the individual stones may move up and down the front slope. The H/ï„D (Stability number) value is more than 2.7 dynamically stable reshaped berm breakwaters (PIANC MarCom, 2003).
3. ARMOUR UNITS
Armour units may be defined as a relatively large quarry stone or concrete shape that is selected to fit specified geometric characteristics and density. It is usually nearly uniform size and large enough to require individual placement. In normal cases it is used as primary wave protection and is placed in thickness of at least two units. Depending on the requirement and availability stones or concrete blocks are preferred.
Armour units are broadly classified as natural armour units and artificial armour units.
Stones come under natural armour units and concrete units under artificial armour units.
3.2 Artificial armour units
In the early days stones were used as armour layer units since the construction of breakwater was limited to shallow waters. As the construction moved towards deeper sea, the weight of armour stone required also increased. It became difficult to procure such heavy weight stones or even to transport them to the site. Sometimes such heavy weight armour stones were not available in the nearby quarries. This posed a problem as breakwaters constitute the main part of the port from economic point of view. In order to overcome this disadvantage and with the advancement in the field of concrete technology a new type of armours were developed known as artificial armour units.
These are defined as the concrete blocks of various shapes and sizes cast based on the requirement in the site. The artificial armour units have advantages like they can be of desired shape, size and weight, also can attain better interlocking capability, improved hydraulic and structural stability and can be cast in-situ. The blocks find a stable position on the slope. Their optimum interlocking capability is balanced between hydraulic stability and the ease of fabrication. All these features make artificial armour unit a better alternative for natural stone.
A large variety of concrete breakwater armour units have been developed in the past 50 years. Today design engineers have the choice between a numbers of completely different breakwater armour concepts. However, the units developed are mainly site specific and problem specific. A large variety of concrete armour units has been developed in the period 1950-1970 (see Fig. 1.2). Table 3.1 gives the historical development of some of the artificial armour units.
The engineers on site found that artificial blocks were always less stable than natural rocks of the same unit weight most of the times (Danel, 1953). The most characteristic phenomena that were seen such as uplifting of armour blocks due to the effect of wave up-rush, internal pore pressure and down-rush. In order to overcome this, series of tests were conducted by Danel in 1950 which led to the development of new types of artificial armour units like Tetrapods. Danel (1953) summarized the characteristics required for such a block as under:
Porosity: Breakwater layers should not be impervious because of the possibility of occurrence of internal pressures in the mound causing the disruption of this layer. Pervious armour blocks tend to dissipate the internal pressure. In addition, a permeable layer is also desired from the point of view of dissipation of incident wave energy and reduction of run-up, run-down and overtopping. The blocks should not provide a continuous facing and should have as few large plain surface as possible.
Table 3.1 Historical development of selected artificial armour units
(Ref: Bakker, 2003)
Roughness: Roughness of the armour layer surface is desirable in order to dissipate the energy of incident waves and reduce overtopping. Thus friction between the water layer and the mound is increased. It is also desirable to increase the friction of the mound by promoting interlocking of the blocks of the armour layer. The above two effects can be achieved by a block having projections which will ensure both, a rough external facing and satisfactory interlocking of the blocks.
Resistance: The blocks must also have adequate resistance against breakage. Thus an optimum length of these projections is needed. Many studies have been carried out in the subject of mechanics of forces exerted on the breakwater, particularly on the armour blocks. Many armour units were developed of varied shapes but with a number of outstanding legs in order to increase resistance between the units.
The slender armour units 'Dolos' developed by Merrifield in South Africa in 1968 probably represents the peak of this concept and has a very high degree of interlocking.
The failure of the Sines breakwater (Portugal) and the introduction of the Accropode by Sogreah in 1980 set an end to the rapid development of randomly placed concrete armour units. The breakwater at Sines was initially designed with 42t Dolos and later rebuilt with Antifer Cubes. The failure indicated that (a) slender armour units, which are designed for maximum interlocking, provide insufficient structural stability and (b) breakage of armour units may cause progressive failure.
A parallel development of completely different type of armour concept started in the late 1960's. The armour layer consisting of hollow blocks that are placed uniformly in a single layer (cobblestone-concept) where each block is tied to its position by the neighbouring blocks. This armour concept is not based on weight or interlocking but on friction, which provides an extremely high hydraulic stability.
Later studies by investigators have shown that voids play a very important part in the stability of armour layers. It is in these voids, created by units in a pack, that the greatest dissipation of wave energy takes place i.e. voids are a way of relieving fluid pressure trying to move the blocks. For certain geometric shapes, the percentage of voids in the armour layer increases drastically as compared to conventional rectangular block armour layers. The Dolos armour unit, basically designed on the concept of interlocking has a void ratio of almost 60%, which may be a significant factor contributing to its very high stability factor.
Later, based on void ratio new type of armour units have been designed which are called the hollow block single layer design. These are of various forms e.g. COB, SHED etc. The units are required to be placed regularly in a single layer on the exposed slope of the breakwater. Inter block friction along with the voids play a major part in the stability of these units. The units have performed very well under ideal laboratory conditions and have exhibited very high stability. However, the main drawbacks are listed below.
The main difficulty is the establishment of approximate design criteria since the definition of the stability coefficient on the basis of Hudson's approach is not applicable.
The other major limitation is the practical considerations of provision of an absolutely fixed base to the armour layer, an even under layer on which these units are to be placed, a mound that will not exhibit appreciable differential settlement, good quality control so that no defective blocks are used. Finally, necessary placement techniques to ensure that each unit is located correctly without any damage.
An added problem would be the removal of core and under layer material through the large voids of armour layer due to wave action. Careful gradation of the filter layer would be an essential requirement, making the construction complicated.
From careful examination of the above points it can be concluded that, the development of artificial armour units started with the need for higher armour weight which could not be provided by natural stone units. The emphasis is then shifted to the concepts of porosity and interlocking. With the present emerging concepts of structural strength, stability and voids, it seems that much new design of armour units say, parallelepiped blocks, Dolos, Tetrapods, Accropodes, and Core-loc were evolved.
3.3 Classification of artificial armour units
Bakker (2003) classified the concrete blocks based on risk of progressive failure as:
Compact blocks: The stability is mainly due to the own weight. The average hydraulic stability is low. However, the structural stability is high and the variation in hydraulic stability is relatively low. Thus, the armour layer can be considered as a parallel system with a low risk of progressive failure.
Slender Blocks: The stability is mainly due to interlocking and the average hydraulic stability is large. However, the variation in hydraulic resistance is also relatively large and the structural stability is low. Therefore, slender blocks shall be considered as a series system with a large risk of progressive failure.
Further, breakwater armour units can be classified based on their shape as shown in Table 3.2.
Table 3.2: Classification of breakwater armour units by shape
(Ref: Bakker, 2003)
Cube, Antifer Cube, Modified Cube, Grobbelar, Cob, Shed
Dolos, Akmon, Toskane
Tetrapod, Tetrahedron (solid, perforated, hollow), Tripod
2-D: Accropode, Gassho, Core-Loc
3-D: Hexapod, Hexaleg, A-Jack
Slab type (various shape)
Tribar, Trilong, N-Shaped Block, Hollow Square
A more general classification of armour units that comprises shape, stability and placement pattern divides the most commonly used armour units in to 6 categories as shown in Table 3.3 below.
Table 3.3: Classification of armour units by shape, placement and stability factor
(Ref: Bakker, 2003)
Number of layers
(1) Cube, Antifer
(2) Tetrapod, Akmon, Tribar, Tripod
(3) Stabit, Dolos
(4) A-Jack Accropode, Core-Loc
(6) Seabee, Hollow cube, Diahitis
Finally based on their placement pattern they may be classified as,
1) Randomly placed armour units - stability factors weight and interlocking
a) First generation armour units
i) The units have a simple shape; the stability factors are weight and to very limited extend interlocking. The placement is random in 2 layers. Typical examples are Cube, Antifer Cube, Modified Cube etc.
ii) First generation armour units that are placed randomly in a single layer are currently investigated ('Single-Layer-Cubes').
b) Second generation armour units
i) Simple shape: Stability factors are weight and to some extent interlocking. The placement pattern is mostly random and in 2 layers. Typical examples are Tetrapod, Akmon, Tribar, Tripod, etc.
ii) Complex shape: The governing stability factor is interlocking; the placement is random in 2 layers. Typical units of this type are Stabit and Dolos.
c) Third generation armour units
The units are placed randomly in a single layer. The shape varies from relatively simple (A-Jack) to complex (Accropode and Core-Loc). The governing stability factor is interlocking.
2) Uniformly placed armour units - stability factor friction
a) Parallel-epipedic hollow blocks with either simple (Seabee, Hollow Cube and Diahitis) or complex shape (Cob and Shed). The placement is uniform in a single layer (cobblestone-concept). The governing stability factor is interlocking.
Table 3.4 List of breakwaters constructed using artificial armour units in India
(Ref: International Breakwater Directory accessed on 20/07/2012)
Type of units
Breakwaters at Androth islands of Lakshadweep, India
Breakwater protecting LNG terminal in Dahej, India
Main breakwater at Colachel, India
Breakwater protection works at Ennore coal port, Chennai
Main breakwater at Gangavaram deepwater port, Andhra Pradesh
Roundheads of breakwaters in Kattupalli shipyard, Chennai
Repair work in East breakwater of Tuticorin port, Chennai
L-shaped breakwater at Kalpeni, Lakshadweep
Pawas bay export facility - 600 ml new breakwater for a private export port on the west coast of Maharastra
Core - Loc
Construction of 2 breakwaters for the Hazira LNG terminal
Jaigarh port - Greenfield all weather port facility at Dhamankul bay in Ratnagiri state (west coast) - Protection of the main breakwater
Thengapatinam Fishery harbour located on the south west coast of India (Tamil Nadu state, kanyakumari district)
Core - Loc
In this chapter previous studies on breakwaters are reviewed with the interest of finding the recent developments and innovations. The various methods adopted and their shortcomings are stated.
The berm breakwaters built using smaller stones and available quarry yield economically there can be 50 to 70% cost savings compared to traditional breakwater (Baird and Hall, 1984).
Hall and Kao (1990) from their studies on dynamically stable berm breakwater concluded that the wave height is the single most important factor affecting the reshaping process. Also, they found that wave period and wave groupiness had no significant effect on eroded berm width, width of toe and volume of armour stones in the front slope.
It has been observed in physical model that the most common displacement mechanism for individual armour stone piece is of a rotational nature (80%) (Norton and Holmes, 1992) and may occur during the reshaping of the berm and later for dynamically stable berm breakwater (Tomasicchio et al., 1994).
Hegde and Srinivas (1995) carried out studies with different porosity of the core of a rubble mound breakwater. They found that the damage increases with a decrease in core porosity.
Lissev and Torum (1996) based on their study concluded that the core can be extended into the berm of a berm breakwater. Since the core material is generally cheaper than the armour stones, the concept of extending the core material into the berm will give a cheaper berm breakwater structure.
Torum et al. (1999) stated that it is acceptable for the berm to reshape. However, the residual berm width should not be less than 4*Dn50. After reshaping the distance from the reshaped profile to the lower layer with smaller stones, possibly a filter layer should be larger than 1.5Dn50 or at least 2 m.
Triemstra (2000) conducted studies on rubble mound breakwaters with high density concrete with cube as armour units. He concluded that the high-density concrete elements behave based on stability formulae. The linear relation between Hs/D and Î” in stability formulae for breakwater armour elements is still valid for densities up to 4000 kg/m3.
There will be natural sorting of the stones that leaves smaller stones in the most exposed area of the slope of the breakwater. So, even if some stones are broken, even on the upper part of the slope, especially for the reshaped statically stable berm breakwater there is no danger of damage to the structure (Torum et al., 2002).
Subba Rao et al. (2008) from their experimental study found out that damage of a non-reshaped berm breakwater was relatively significant for shorter period waves in comparison with longer period waves, in the range of wave steepness (Ho/Lo) from 0.043 to 0.008. Further, they found that the fluctuation in water level above the berm influenced the stability of the berm.
It was found that breaking waves would cause more significant damage to the structure compared to non-breaking waves. Further, they stated that breakwater could suffer severe damage much before Rec=B when berm is located below SWL but when berm is below SWL it was seen that recession was much lower. Also scale effects on reshaping profiles are not a major problem and are almost negligible for Reï‚³3*104 (Lykke Andersen and Burcharth, 2010).
Moghim et al. (2011) stated that dimensionless wave period (To) is an important parameter for reshaping in a berm breakwater and also suggested that the combined effect of wave height and wave period should be considered to study the stability of the structure. Regarding the berm width they concluded that initial berm width has no much significance on the reshaping of armour layer and berm recession. With respect to berm position they observed that if the berm elevation from still water level is increased the berm recession was found to be decreasing.
For (regular) surging waves above Î¾ > 4.0 the surface roughness has a negligible influence on the reduction of the wave run-up. For Î¾ < 4.0 both the surface roughness and the permeability of the armour layer have an influence on the wave run-up (Van Broekhoven, 2011).
Torum et al. (2012) have compared various formulae for the recession of berm with their experimental results and found that Lykke Andersen (2006) formula is more reliable for deep water cases although Torum (2007) formula seems to work good for deep water homogenous berm breakwater.
4.1 Berm Recession
An important feature of reshaping is the recession of the berm. Torum (1998) and Torum et al. (1999) gave the dimensionless recession, Rec/Dn50, when the waves are approaching the breakwater almost normal to the breakwater longitudinal axis as
Rec/Dn50 = 0.0000027(HoTo)3 + 0.000009(HoTo)2 + 0.11(HoTo) - 0.8 ------------ (4.1)
Later Menze (2000) and Torum and Krogh (2000) added terms to take into account the gradation of the stones and the water depth. The recession equation arrived at is then:
Rec/Dn50 = 0.0000027(HoTo)3 + 0.11(HoTo) - (- 9.91fg2 + 23.9 fg - 10.5) - fd ------ (4.2)
and is valid for 1.3 < fg < 1.8,
where, fd= Depth factor = - 0.16(d/Dn50) + 4.0, within the range 12.5 < d/Dn50 < 25
HoTo = Wave period stability number
Ho = Stability number
To = Wave period stability number =
Tz = Mean wave period
d = Water depth in front of the berm breakwater.
Moghim et al. (2011) suggested replacing HoTo by a new term in the recession equation and gave the following new equation.
for --------------------------- (4.3)
for ------------------------ (4.4)
The equations are valid within the following range of variables,
; 500 < N < 6000; 1.2 < fg < 1.5;
d/L < 0.25; 8.0 < d/Dn50 < 16.5; 0.12 < hbr/Hs < 1.24.
Various authors have done studies related to the position of berm and berm widths. Many formulae have been suggested by different authors to compute recession which are substantiated with model studies. The economic advantage of berm breakwater is nicely depicted by various authors in the literature. The literature review gave a brief idea about the design parameters of berm breakwaters. However, it is found that there is not design formula to calculate reduced weight of the armour units for berm breakwaters like Hudson formula, Vander Meer formula etc. which are used for conventional rubble mound breakwater. Presently, same formulae are being used to calculate the weight of armour unit for berm breakwater and then applying some percentage reduction, physical model studies are conducted in laboratories before construction. Further, no formula has been derived yet to decide the width and position of the berm.
OBJECTIVES OF THE PRESENT STUDY
From the literature it is found that there is no definite design procedure or formulae for finalising the various structural dimensions of a statically stable reshaping breakwater. Further, no work is carried out on berm breakwaters with artificial armour units. Keeping in mind the above points the following objectives are defined.
Static stability of breakwater for reduced armour weights.
Influence of fluctuation in still water level on the static stability of berm breakwater.
Influence of berm width on the reshaping of statically stable reshaped breakwater.
To evolve optimal design of statically stable reshaped berm breakwater.
The experiments are conducted on the statically stable berm breakwater structure with concrete cubes as armour units.
Series of experiments are conducted consisting of testing the stability of the statically stable reshaped berm breakwater for different wave parameters in the regular wave flume facility available in NITK, Surathkal.
The wave climates off the Mangalore coast as given by KREC Study Team (1994) are considered while planning the present experimental investigation. During the monsoon, the maximum recorded wave height off Mangalore coast is 6.5 m. During fair weather season wave height seldom exceeds 1m. Predominant wave period is 8 to 12 s. Occasionally, during the fair weather season, wave periods up to 15 s are observed. Hence, for the design of berm breakwater model an equivalent of prototype design wave of height 3 m is assumed, while a wave equivalent of height up to 4.8 m and period of 8 to 14 s are considered for the model study.
6.1 Experimental facility
The wave flume is of 50 m length, 0.71 m width and 1.1 m depth (Fig. 6.1). It has a 42 m long smooth concrete bed. About 25 m length of the wave flume is provided with glass panels on one side to facilitate observations and photography. It is provided with a bottom hinged flap which is moved to and fro by an induction motor of 11 KW, 1450 rpm at one end. The wave filter consists of a series of vertical asbestos sheets spaced at about 10 cm distance from each other and kept parallel to the length of the flume. Capacitance type wave probes are used for recording the data. The flume is provided with iron railings on the top of the sidewalls to enable the movement of a trolley carrying the sounding rods or wave profiler mechanism system along the flume which is used to obtain the profile of structure.
Fig. 6.1 Model in Wave flume facility
6.2 Calibration of experimental set-up
Calibration of the experimental set up and instruments were undertaken frequently to check and ensure accuracy. The method of calibration of each component is given below.
6.2.1 Wave flume
The wave flume is filled with fresh water to the required depths (d) of 0.30 m, 0.35 m, 0.40 m and 0.45 m. Regular waves of height (H) of 0.10 m, 0.12 m, 0.14 m and 0.16 m with varying periods (T) of 1.6 s, 2.0 s and 2.6 s are generated. Before starting the experiment, the flume is calibrated to produce the incident waves of different combinations of wave height and wave periods. Combinations that produced the secondary waves in the flume are not considered for the experiments. During the experiment, the waves are recorded by the probes which are set before and after the breakwater. The wave probes are calibrated at the beginning and at the end of the test runs. The signals from the wave probes are recorded. The incident and reflected wave heights are separated using the readings of the first three probes and the transmitted wave heights were directly measured using the fourth probe. Incident and transmitted wave heights are also measured manually and crosschecked with the instrumental data and found to be matching well.
6.2.2 Wave probes
The wave probes work based on the principle of electrical conductance. The primary output is in the form of voltage which varies from -3 V to 3 V. The embedded software in the wave recording system converts it to water level variations. The probes were originally calibrated by the manufacturer. However, the output is expected to show minor variations depending on the salinity and temperature of the water used in the flume. Hence the probes are subjected to static immersion tests and the relationship between the water level and the output voltage is determined and recorded. The variation of voltage with water level is shown in Fig. 6.2. The calibration is undertaken daily before and after the experiments to find the gauge correction factor.
Probe 1C:\Users\User\AppData\Local\Microsoft\Windows\Temporary Internet Files\Content.Word\New Picture.png C:\Users\User\AppData\Local\Microsoft\Windows\Temporary Internet Files\Content.Word\New Picture (1).png
Probe 3C:\Users\User\AppData\Local\Microsoft\Windows\Temporary Internet Files\Content.Word\New Picture (2).png
Fig. 6.2 Calibration of wave probes, water level vs. Voltage with respect to midpoint of the probe
6.3 Dimensional analysis
Many problems involving fluid motions are quite complex in nature. In the present case the complex flow phenomenon responsible for energy dissipation cannot be easily represented by mathematical equations and one has to rely on experimental investigations. The results of such investigations are more useful when expressed in the form of dimensionless relations. To arrive at such dimensionless relations of different variables, dimensional analysis is carried out. Dimensional analysis is a rational procedure for combining physical variables into dimensionless parameters, thereby reducing the number of variables that need to be considered. Following are the predominant variables influencing the stability of breakwater.
For deep water wave conditions L and T are related by the equation,
The term gT2 is incorporated in the following equation to represent the wave length L, instead of taking L directly. This is because, if L is used it would be depth specific, while gT2 is independent of depth and represents the deep water wave characteristics which can be easily transformed to shallow waters depending on local bathymetry.
Table 6.1 Predominant variables affecting the stability of breakwater
Deep water wave height (Ho)
Water depth (d)
Wave period (T)
Wave length (L)
Run up (Ru)
Run down (Rd)
Armour weight (W)
Nominal diameter (Dn50)
Position of the berm (hb)
Thickness of armour layer (ta)
Berm width (B)
Mass density (Ï)
Dynamic viscosity (v)
Acceleration due to gravity (g)
After conducting the dimensional analysis using Buckingham's-Ï€ theorem the following dimensionless parameters were obtained:
Period stability number HoTo
Stability Number (Ns) Hs/Î”Dn50
Surf similarity parameter Î¾eq
Relative berm position hb/d
Relative water depth d/gT2
Deepwater Wave steepness Ho/gT2
Dimensionless wave run-up Ru/Ho
Dimensionless wave run-down Rd/Ho
Dimensionless Recession Rec/Dn50 & Rec/B
The term Ho in period stability number indicates wave height stability which is the stability number (Ns).
6.4 Similitude criteria and model scale selection
In the method of dimensional analysis, similitude is achieved between the prototype and the model with the help of non-dimensional parameters of the phenomenon. These non-dimensional parameters must be of the same range for both the model and the prototype. In the present study similitude is achieved by considering the non-dimensional parameter- deepwater wave steepness, Ho/gT2 (Table 6.2).
Table 6.2 Wave parameters of prototype and model
1 to 6.5
8 to 14
0.00046 to 0.01132
0.033 to 0.217
1.46 to 2.556
0.000456 to 0.011347
The choice of scale, for the model test, is often limited by constraints put by experimental facilities available. Within this constraint, an optimum scale should be selected by comparing the economies of the scale model with that of the experiment (Hughes, 1993 and Chakrabarti, 1996). As the general rule, the model should be as large as possible.
To simulate the field conditions of wave height, period and water depth, by the application of Froude's Law (Hughes, 1993) a geometrically similar scale of 1:30 was selected. For this scale the similitude condition is satisfied (Table 6.3). This scale is within the scale selected for rubble mound breakwater model tests conducted in majority of the laboratories around the world and is good enough to give reasonable and satisfactory results compared to those of the prototype (Losada, 1991, Hughes, 1993).
Table 6.3 Selection of model scale
6.5 Breakwater Model
The breakwater model consists of three layers namely primary layer, secondary layer and core. The armour weight for the primary layer (W50) is calculated using Hudson formula (Eq. 6.2) for a design wave height of 3m in field. The weight of secondary layer and core is then estimated as W50/10 and W50/100 respectively. The thickness of primary layer and secondary layer is computed using Eq. 6.3 and Eq. 6.4. The slope of breakwater section on both the sides 1V: 1.5H. The design procedure is as follows,
Where, ï§r = mass density of armour unit = 2.4 g/cc
H = design wave height = 10 cm (model)
KD = Stability co-efficient = 5.5
KD of cubes =8.3 / 1.5 = 5.5
ï„ = relative mass density = (ï§r/ï§w-1)
ï§w = density of water = 1 g/cc
cotï¡ = breakwater slope =1.5
Primary armour layer thickness (tp),
Where, n = no. of primary layers
Kï„ = layer stability co-efficient (Concrete cube = 1.11)
Secondary armour layer thickness (ts),
The table below gives the reduced weights and respective armour layer thickness.
Table 6.4 Percentage reduction in weight of armour and layer thickness
Percentage reduction in weight
Primary armour weight (W50) (gms)
Secondary armour weight (gms)
Primary armour layer thickness (cm)
Secondary armour layer thickness (cm)
J:\New folder\New Picture.png
Fig. 6.3 Typical cross-section of berm breakwater model
6.6 Range of experimental variables
Table 6.5 Range of variables
10, 12, 14 &16 cm
1.6, 2.0 & 2.6 sec
30, 45 cm
Angle of wave attack
30, 35, 40 & 45 cm
Shape of armour units
Design Armour unit weight
79.5, 63.6 & 53 gm
Nominal diameter of primary Armour unit
3.25, 2.98 & 2.85 cm
Crest height and width
70 cm & 15 cm
Specific gravity of armour unit
6.7 Physical properties of armour units
Bulk density - The bulk density of the armour units calculated and the average value of bulk density is found to be 2.40 gm/cc, accordance with the IS 2386 (part-III)- 1963.
Specific gravity - The specific gravity of the concrete cube armour used as primary armour unit is determined. Five samples were taken and the specific gravity calculated as 2.4.
Porosity - The Porosity of the primary armour was found to be 47%, and that of the core is 49 %.
6.8 Tests conducted on materials
â€¢ Standard consistency = 30%
â€¢ Initial setting time = 50 minutes
â€¢ Final setting time = 330 minutes
â€¢ Specific gravity of Cement= 3.1
â€¢ Specific gravity = 2.64
â€¢ Fineness modulus = 3.4
â€¢ Cement mortar = 1:3
â€¢ Water cement ratio = 0.4
â€¢ Proportion of sand and iron ore = 80:20
â€¢ Compressive strength of cube in 28 days = 37.1N/mm2
The measurements involved in the present investigation include wave height, wave period, wave run-up, wave run-down and damage profiling.
6.9.1 Measurement of wave height and wave period
The calibration of flume is done and the stroke of the wave flap may be changed by changing the eccentricity of the flywheel generating waves with varying wave heights. The wave heights and wave period are measured with the wave probe and the data collected is converted into digital form with ADC card and checked manually. The probes are calibrated before using. Speed of the motor is varied by changing the frequency input through the inverter. The wave period measured by probes and the average of total time required for five revolutions of flywheel of the motor is counted manually by wheel rotation.
Fig. 6.4 Measurement of wave height and wave period using wave probes
6.9.2 Measurement of wave run-up and wave run-down
The markings on graph sheet made on the sloping line of the breakwater structure above and below the still water level help in recording water level changes for manual verification. Wave run-up is measured by noting the vertical distance above the still water level reached by the up rushing water when a wave impinges on the test structure. Wave run-down is measured by noting the vertical distance below the still water level reached by the down rushing water. Average of 30 observations in the initial part of each test run is considered for analysis.
6.9.3 Quantification of damage of Breakwater
The recession of the berm and the exposure of secondary layer on the sea side slope reflect the damage to the structure. If Rec/B (dimensionless recession number) is less than one then structure is safe otherwise unsafe. Further, the structure is considered damaged with the exposure of secondary layer. Sounding rods are used for obtaining initial profile of the breakwater before the test and the final profile of the breakwater after the test is recorded.
6.10 Experimental Procedure
The initial sea side profile of the breakwater was taken before starting the experiment. The incident wave height was measured at a distance 1m from the main breakwater. After every five waves, the wave generator was stopped to avoid multiple reflections. The storm duration of 3000 waves is the limit for every test run. With the exposure of the secondary layer and recession exceeding berm width, the breakwater section was considered to have failed. Profiling of the damaged section was carried out using surface profiler system at specific location marked over the wave flume. The recession is calculated and damage number (Nod) was computed by manually counting the number of cube displaced from the berm during experiment. Model is rearranged after each completed run and the experiment is repeated for other wave parameters.
RESULTS AND DISCUSSION
The experiments are conducted with reduction in artificial armour unit weight by 25%, 40% and 50%. The effect of various parameters like deepwater wave steepness, stability number, surf similarity parameter on berm recession, damage number, wave run-up and wave run-down are explained.
7.1 25% armour weight reduction
7.1.1 Effect of stability number on recession
Fig. 7.1 shows the effect of stability number (Ns) on dimensionless wave recession (Rec/B). With the increase in Ns a gradual increase in recession can be seen in the graph. Also with the increase in B/d ratio the recession is found to increase. For all the values of Ns, Rec/B is less than one in case of B/d =1.0-1.5 (B =0.45 m). For B/d =0.67-0.86 (B =0.30 m) same is not seen as for some of the stability numbers (Ns =2.2, 3.1, 3.6), Rec/B has reached a value of one. The structure is safe (Rec/B<1) for lower stability number of Ns =2.2 (H =0.10m) for both the range of B/d values. For Ns =3.6 and B/d =0.67-0.86 the Rec/B is equal to one for all the parameters considered. From above discussion it can be retrieved that B/d =1.0-1.50 is safe with respect to recession criteria for 25% reduction in weight.
Fig. 7.1 Effect of Stability number (Ns) on Berm recession (Rec/B) for different berm widths
7.1.2 Effect of stability number on damage number
Fig. 7.2 Influence of Stability number (Ns) on Damage number (Nod) for different berm widths
The effect of stability number (Ns) on damage number (Nod) for 25% reduction in armour weight is rendered in graph 7.2. It can be seen that with the increase in Ns the Nod also increases gradually for both the B/d cases. For Ns =2.2 and B/d =1.0-1.50, Nod value is less than 2 for all wave periods and water depths. For B/d =1.0-1.50, a maximum Nod of 9.4 is reached for Ns value of 3.6 (H =0.16 m). In case of B/d =0.67-0.86, Nod ranges from 2.4 to 19.8 for all Ns values. From the above discussion it can be showed that B/d =1.0-1.50 is safer than B/d =0.67-0.86.
7.1.3 Effect of surf similarity parameter on wave run-up
Fig. 7.3 (a), (b) and (c) represent the variation of dimensionless wave run-up (Ru/Ho) with surf similarity parameter (ï¸eq) for various water depths of d/gT2 = 0.007-0.018 (d=45cm), 0.006-0.016 (d=40cm), 0.005-0.014 (d=35cm) respectively. An increasing trend for wave run-up with the increase in surf similarity parameter can be seen in all the graphs. Also the wave run-up is lower for 45 cm berm width compared to 30 cm berm width in all the graphs. This is due to presence of large area for dissipation of wave energy thus reducing run-up of the waves.
In Fig. 7.3(a) the wave run-up varies from 0.921 -1.370 and 0.886 -1.231 for 30 cm (B/d=0.67) and 45 cm (B/d=1.0) berm width respectively. For 45 cm berm width there is 4% -10% reduction in wave run-up compared to 30 cm berm width.
In Fig. 7.3(b) the wave run-up varies from 0.959 -1.383 and 0.759 -1.183 for 30 cm (B/d=0.75) and 45 cm (B/d=1.13) berm width respectively. For 45 cm berm width there is 15% -21% reduction in wave run-up compared to 30 cm berm width.
In Fig. 7.3(c) the wave run-up varies from 1.196 -1.548 and 0.959 -1.348 for 30 cm (B/d=0.86) and 45 cm (B/d=1.29) berm width respectively. For 45 cm berm width there is 13% -20% reduction in wave run-up compared to 30 cm berm width.
Fig. 7.3 Influence of Surf similarity parameter (ï¸eq) on wave run-up (Ru/Ho) for different water depths
From the above graphs it can be concluded that with the berm width and the position of berm influences the wave run-up. With the increase in berm width there is decrease in wave run-up and for a berm position of 0.05m to 0.10m above SWL produces lesser run-up compared to a berm position equal to SWL.
7.1.4 Effect of surf similarity parameter on wave run-down
Fig. 7.4 (a), (b) and (c) represent the variation of dimensionless wave run-down (Rd/Ho) with surf similarity parameter (ï¸eq) for various water depths of d/gT2 = 0.007-0.018 (d=45cm), 0.006-0.016 (d=40cm) and 0.005-0.014 (d=35cm) respectively. An increasing trend for wave run-down with the increase in surf similarity parameter can be seen in all the graphs. Also the wave run-down is lower for 45 cm berm width compared to 30 cm berm width in all the graphs. This is due to presence of large area for dissipation of wave energy thus reducing down rush of the waves.
Fig. 7.4 Influence of Surf similarity parameter (ï¸eq) on wave run-down (Rd/Ho) for different berm widths
In Fig. 7.4(a) the wave run-down varies from 0.927 -1.134 and 0.675 -0.888 for 30 cm (B/d=0.67) and 45 cm (B/d=1.0) berm width respectively. For 45 cm berm width there is 22% -27% reduction in wave run-down compared to 30 cm berm width.
In Fig. 7.4(b) the wave run-down varies from 0.959 -1.383 and 0.759 -1.183 for 30 cm (B/d=0.75) and 45 cm (B/d=1.13) berm width respectively. For 45 cm berm width there is 18% -23% reduction in wave run-down compared to 30 cm berm width.
In Fig. 7.4(c) the wave run-down varies from 1.196 -1.548 and 0.959 -1.348 for 30 cm (B/d=0.86) and 45 cm (B/d=1.29) berm width respectively. For 45 cm berm width there is 10% -11% reduction in wave run-down compared to 30 cm berm width.
From the above discussion it can be concluded that with the berm width and the position of berm influences the wave run-down. With the increase in berm width there is decrease in wave run-down and for a berm position of equal to SWL produces lesser run-down compared to a berm position more than SWL. This is due to the fact that when berm position is more than SWL the wave plunges directly on the lower slope which does not dissipate much energy as in case when berm position is equal to SWL where wave plunges on berm dissipating its most of the energy.
7.2 40% armour weight reduction
7.2.1 Effect of stability number on recession
Fig. 7.5 shows the effect of stability number (Ns) on dimensionless wave recession (Rec/B). From the graph it can be seen that for a value of Ns =2.5, Rec/B is less than 1 for both the cases of B/d =1.0-1.5 (B =0.45 m) and B/d =0.67-0.86 (B =0.30 m). Few models with higher Ns values of 3.0, 3.5 and 4.0 have reached a value of Rec/B =1, for a wave period of 1.6s (ï¸eq =1.3-1.6). Also for B/d =1.0-1.50 for a wave period of 2.6s (ï¸eq =2.2-2.8), Rec/B <1. For Ns =4.0 and B/d =0.67-0.86 the Rec/B is equal to 1 for all the parameters considered. From above discussion it can be retrieved that B/d =1.0-1.50 is safe with respect to recession criteria for Ns value of 2.5 and further shorter period waves causes more damage compared to longer period waves.
Fig. 7.5 Effect of Stability number (Ns) on Berm recession (Rec/B) for different berm widths
7.2.2 Effect of stability number on damage number
Fig. 7.6 Influence of Stability number (Ns) on Damage number (Nod) for different berm widths
The effect of stability number (Ns) on damage number (Nod) for 40% reduction in armour weight is exhibited in graph 7.6. It can be seen that with the increase in Ns the Nod also increases for both B/d cases. For Ns =2.5, wave period of 2.6s and B/d =1.0-1.50, Nod value ranges from 0 to 2.1 and for wave period of 1.6s Nod ranges up to 7.9 for all water depths. In case of B/d =0.67-0.86, Nod ranges from 2.7 to 19.8 for all Ns values. From the above discussion it can be showed that B/d =1.0-1.50 is safer than B/d =0.67-0.86 and also shorter period waves causes more damage compared to longer period waves.
7.2.3 Effect of surf similarity parameter on wave run-up
Fig. 7.7 (a), (b), (c) and (d) represent the variation of dimensionless wave run-up (Ru/Ho) with surf similarity parameter (ï¸eq) for various water depths of d/gT2 = 0.007-0.018 (d=45cm), 0.006-0.016 (d=40cm), 0.005-0.014 (d=35cm) and 0.005-0.012 (d=30cm) respectively. An increasing trend for wave run-up with the increase in surf similarity parameter can be seen in all the graphs. Also the wave run-up is lower for 45 cm berm width compared to 30 cm berm width in all the graphs.
Fig. 7.7 Influence of Surf similarity parameter (ï¸eq) on wave run-up (Ru/Ho) for different berm widths
In Fig. 7.7(a) the wave run-up varies from 1.142 -1.847 and 0.952 -1.480 for 30 cm (B/d=0.67) and 45 cm (B/d=1.0) berm width respectively. For 45 cm berm width there is 17% -20% reduction in wave run-up compared to 30 cm berm width.
In Fig. 7.7(b) the wave run-up varies from 0.940 -1.789 and 0.673 -1.407 for 30 cm (B/d=0.75) and 45 cm (B/d=1.13) berm width respectively. For 45 cm berm width there is 21% -29% reduction in wave run-up compared to 30 cm berm width.
In Fig. 7.7(c) the wave run-up varies from 0.968 -1.736 and 0.538 -0.903 for 30 cm (B/d=0.86) and 45 cm (B/d=1.29) berm width respectively. For 45 cm berm width there is 45% -48% reduction in wave run-up compared to 30 cm berm width.
In Fig. 7.7(d) the wave run-up varies from 1.246 -1.70 and 0.529 -1.134 for 30 cm (B/d=1.0) and 45 cm (B/d=1.50) berm width respectively. For 45 cm berm width there is 33% -58% reduction in wave run-up compared to 30 cm berm width.
From the above discussions it can be concluded that with the berm width and the position of berm influences the wave run-up. With the increase in berm width there is decrease in wave run-up and for a berm position of 0.10m to 0.15m above SWL produces lesser run-up compared to other berm positions.
7.2.4 Effect of surf similarity parameter on wave run-down
Fig. 7.8 (a), (b), (c) and (d) represent the variation of dimensionless wave run-down (Rd/Ho) with surf similarity parameter (ï¸eq) for various water depths of d/gT2 = 0.007-0.018 (d=45cm), 0.006-0.016 (d=40cm), 0.005-0.014 (d=35cm) and 0.005-0.012 (d=30cm) respectively. An increasing trend for wave run-down with the increase in surf similarity parameter can be seen in all the graphs. Also the wave run-down is lower for 45 cm berm width compared to 30 cm berm width in all the graphs.
In Fig. 7.8(a) the wave run-down varies from 0.871 -1.299 and 0.805 -1.051 for 30 cm (B/d=0.67) and 45 cm (B/d=1.0) berm width respectively. For 45 cm berm width there is 8% -19% reduction in wave run-down compared to 30 cm berm width.
In Fig. 7.8(b) the wave run-down varies from 0.835 -1.244 and 0.813 -1.020 for 30 cm (B/d=0.75) and 45 cm (B/d=1.13) berm width respectively. For 45 cm berm width there is 3% -18% reduction in wave run-down compared to 30 cm berm width.
Fig. 7.8 Influence of Surf similarity parameter (ï¸eq) on wave run-down (Rd/Ho) for different berm widths
In Fig. 7.8(c) the wave run-down varies from 0.848 -1.233 and 0.593 -0.966 for 30 cm (B/d=0.86) and 45 cm (B/d=1.29) berm width respectively. For 45 cm berm width there is 22% -30% reduction in wave run-down compared to 30 cm berm width.
In Fig. 7.8(d) the wave run-down varies from 0.863 -1.143 and 0.753 -0.972 for 30 cm (B/d=1.0) and 45 cm (B/d=1.50) berm width respectively. For 45 cm berm width there is 13% -15% reduction in wave run-down comp