Breakwater Design Assignment

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The University of New South Wales Coastal Engineering – CVEN9640 Assessment #3 – Breakwater Design Name: Daniel Mangion Date of Submission: 14/04/2023

Table of Contents Introduction ....................................................................................................................... 3 Methodology ..................................................................................................................... 3 Section 1 – Investigating Wave Conditions ......................................................................... 3 Section 2 – Hudson Equation .............................................................................................. 4 Section 3 – Calculating the Cost per Linear Metre of the Breakwater Designs ..................... 9 Section 4 - Van der Meer’s Approach ................................................................................ 10 Section 5 – Consideration of Increased Water Level in the Reservoir ................................. 12 Conclusion ........................................................................................................................ 13 References ....................................................................................................................... 13

Introduction The Australian Water-Skiing Championships are being held in a very long and large water supply reservoir in Southern NSW. A task that has been set out is to develop a preliminary breakwater design parallel to the shore to provide protection and safekeeping for competitors and spectator craft. In order to create the breakwater, it is required to refer to the preliminary studies. Identifying that H s = 1.5 m, T P = 5 s, m = 0.01 and that there is a minimum water depth at the toe of the breakwater to be 1.5 m with a maximum possible surge of 0.1 m. With these values it is required that a satisfactory design of a breakwater is conceptualised with the use of coastal engineering equations, assumptions and a consideration of the materials used. Methodology Creating the preliminary breakwater design for the Australian Water-Skiing Championships will require the use of the preliminary studies and coastal engineering equations to obtain the best suited model for this specific project. The first major equation that will be used to create the breakwater design, is the Hudson equation. It is used to calculate the minimum size armour stone can be to provide the stability characteristics necessary for rubble structures, or in the case more specifically breakwaters at the threat of unknown wave patterns. Within the Hudson equation there are multiple formulas built upon it, which make up features of a breakwater, these include the crest level, primary armour mass/thickness, underlayer mass/thickness and crest width. The crest level is created from the variable run-up formulas that are influenced by the different materials used to make the breakwater, the scaling of these run-up formulas is assumed and can be taken as they are. For the primary and underlayers there are a lot of assumed values based on prior research. Both the stability factor and the number of layers is based on tabulated results. The densities and breakwater slope chosen are assumptions that are made by the coastal engineer determined by what they believe will best suit the breakwater. Lastly, the crest width can be influenced by the construction method used to develop the breakwater or otherwise simplified with a formula to fit the location optimally. All these results can be used to produce a cross- section of the proposed breakwater. The cost per linear metre can be a concern for tradesmen who must buy the materials used for the construction. Furthermore, it is important for engineers to confirm with them the price that these materials will cost prior to when they purchase them, so they can choose the most cost-effective material. Utilising the cross-sectional area of the breakwater and price of each material per tonne, the cost per linear metre of each material can be calculated, therefore simplifying future construction decisions. In order to affirm the results based on Hudson’s equation, the preliminary breakwater design can also be calculated using the Van der Meer approach. Different to the Hudson equation, Van der Meer considers how waves are randomly generated, the types of breaking waves, number of waves in a specific time period and the permeability of the core, when designing a breakwater. The Van der Meer equation has multiple formulas which are chosen based on the surf similarity parameter as it determines whether the breakwater will face plunging or surging waves. The Van der Meer approach still requires multiple assumptions such as that the zero-crossing period is around 70% of the maximum wave period. Since, Van der Meer considers the effect of storm durations in his equation there is also a major assumption that the wave period during these specific time periods is constant, which is unreasonable as during a storm the weather is unpredictable. Nonetheless, with the Van der Meer equation there is another form of affirmation to the results calculated for the preliminary breakwater design. Finally, there is the consideration of increased water level to assess the future complications that the breakwater will face. Within these calculations, once again, there is no consideration for the unpredictability of wave patterns, hence the findings are only purely based on assumptions. To determine the effect of a risen water level it is essential to once again utilise the Hudson equation as the client is after the new required mass of the breakwater. Section 1 – Investigating Wave Conditions To calculate the wave height that will be adopted for the breakwater design, first it is required to find the depth at the toe of the structure. Considering the minimum required water depth and the toe of the breakwater being 1.5 m and the fact that the maximum combined surge/wave setup at the site is 0.1 m. The water depth at the toe of the breakwater ( d s ) is the sum of the surge and minimum water depth (1.5 + 0.1). Therefore d s = 1.6 m. From the preliminary studies it has also been identified

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that the underwater slope of the reservoir is m = 0.01 (1:100). Using figure 1, it is possible to calculate the breakwater height ( H b ) with the abovementioned preliminary results. Figure 1 - Used to estimate the largest wave that will break at the toe of the structure. From figure 1, referring to the m = 0.01 (1:100) line as mentioned above, the y-intercept of the line is approximately equal to 0.9. This value refers to the breakwater height over the depth at the toe of the structure H b d s ¿ = 0.9). Furthermore, to find H b it is possible through rearranging the equation so, H b = 0.9 ×d s = 0.9 × 1.6 = 1.44 m. To determine whether the design wave is expected to be broken or unbroken when it interacts with the breakwater, it is required to analyse the calculations that have just been made. Since H b is 1.44 m and the significant wave height ( H s ) is 1.5 m, H b can be considered the design wave based on it being smaller than H s . Due to the design wave being H b it infers the waves will also be broken when they interact with the front face of the breakwater. In order to find the design wave period, figure 1 can assist in calculating it, using the slope equation H b d s = m× d s ( gT 2 ) , where: - H b is the breakwater wave height (m). - d s is the water depth at the toe of the structure (m). - m is the underwater slope of the reservoir (0.01). - g = 9.81 m/ s 2 . - T is the wave period (s). Rearranging the equation: T = √ md s 2 H b g = √ 0.01 × 1.6 2 1.44 × 9.81 ≈ 0.043 seconds. Therefore, the wave period can be considered as 0.043 seconds.

Section 2 – Hudson Equation Using the Hudson formula, it is possible to construct a complete design of a breakwater. Within this report two alternate designs of breakwaters will be constructed, with quarry stone and tetrapod armour units. a) The crest level is the vertical distance spanning from sea level to the structure’s crest. This height is intentionally made to cover the distance left from the rest of the breakwater. The crest level is determined by its runup equation as it displays the maximum onshore elevation of the wave present. The wave runup is a function of the wave height, wave period, water depth, type of armour, porosity and breakwater geometry. Hence, each armour unit as its own variable equation based on these parameters. (A) Crest level - Quarry stone Run-up (for quarry stone) = 1.2 × H (where H = design wave height) = 1.2 × 1.44 = 1.728 m Hence, the crest level ≥ 1.728 m above the sea water level. (B) Crest level - Tetrapod Run-up (for tetrapod) = 1.0 ×H (where H = design wave height) = 1.0 × 1.44 = 1.44 m Hence, the crest level ≥ 1.44 m above the sea water level. b) The primary armour layer’s role is to protect the inner layers by decreasing the incident wave energy and wave run-up. To design the breakwater, it is necessary to calculate the primary armour’s mass and thickness. Utilising the Hudson equation, the primary mass can be found: M = ρ H 3 K D ∆ 3 cotα , where:  M refers to the mass of the primary armour layer (kg).  ρ refers to the Density of armour ( kg / m 3 )  Δ refers to the Submerged relative density: ρ − ρf ρf , where ρf is the density of freshwater ( kg / m 3 ).  α refers to the breakwater slope (chosen a slope of 1 on 2 or cot α = 2).  H refers to the wave height (found in Q1 to be 1.44 m).  K D refers to the Stability factor or damage coefficient, which can be found in table 1 below:

Table 1 - Suggested K D values for use in determining Armour Unit Weight Through using basic geometric equations, a formula for primary armour layer thickness can be created: r = nK ( M ρ ) 1 3 , where:  r refers to the cover layer thickness (m).  n is the number of layers which can be found in table 1.  K refers to the empirical shape factor, which for preliminary design, we can assume is a ‘cubic’ armour unit shape and hence K ≈ 1.  M refers to the mass of the primary armour layer (kg).  p refers to the density of armour ( kg / m 3 ) (A) Primary Armour (mass and layer thickness) - Quarry stone Calculating the primary armour layer mass:  For the quarry stone armour unit, sandstone will be used to construct it, having a density ( ρ ¿ of 2323 kg / m 3 .  Design wave height (H) is 1.44 m.  K D can be found in table 1 to equal to 2, as from question 1 it was found that the wave is breaking, and it has also been decided to use rough angular quarry stone.  Δ = ρ − ρf ρf , where ρf is the density of freshwater (1000 kg / m 3 ). Δ = 2323 − 1000 1000 = 1.323  ? has a slope of 1 on 2 or cot ? = 2 Hence,

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M = 2323 × 1.44 3 2 × 1.323 3 × 2 ≈ 748.85 kg . Therefore, the primary armour mass of the quarry stone design is 748.85 kg. Calculating the primary armour layer thickness:  n is found in table 1 within the rough angular quarry stone row as n = 2  K is a constant equal to 1  M found as the primary armour mass to be 748.85 kg  ρ is the density of the sandstone found as 2323 kg / m 3 . Hence, r = 2 × 1 × ( 748.85 2323 ) 1 3 ≈ 1.37 m. Therefore, the primary armour thickness of the quarry stone design is 1.37 m. (B) Primary Armour (mass and layer thickness) - Tetrapod Calculating the primary armour layer mass:  For the tetrapod armour unit, concrete will be used to construct it, having a density ( ρ ¿ of 2400 kg / m 3 .  Design wave height (H) is 1.44 m.  K D can be found in table 1 to equal to 7, as from question 1 it was found that the wave is breaking, and through referring to the tetrapod row.  Δ = ρ − ρf ρf , where ρf is the density of freshwater (1000 kg / m 3 ).  Δ = 2400 − 1000 1000 = 1.4  ? has a slope of 1 on 2 or cot ? = 2 Hence, M = 2400 × 1.44 3 7 × 1.4 3 × 2 ≈ 186.55 kg . Therefore, the primary armour mass of the tetrapod design is 186.55 kg. Calculating the primary armour layer thickness:  n is found in table 1 within the rough angular quarry stone row as n = 2  K is a constant equal to 1  M found as the primary armour mass to be 186.55 kg  ρ is the density of the concrete found as 2400 kg / m 3 . Hence, r = 2 × 1 × ( 186 . 55 2400 ) 1 3 ≈ 0.85 m. Therefore, the primary armour thickness of the tetrapod design is 0.85 m. c) The underlayer is the second protective barrier for the core of the breakwater. Just like the primary armour layer, the breakwater design of the underlayer requires a mass and thickness value. The mass of the underlayer can also be referred to as W/10 or one-tenth of the mass of the primary armour layer. To find the thickness of the underlayer it is possible with the Hudson equation used to find the thickness of the primary armour layer. All values can be perceived to be the same, except for the mass which is one-tenth of the respective primary armour layer. (A) Underlayer (mass and layer thickness) – Quarry stone Calculating the underlayer mass ¿ 1 10 × primary armourmass

¿ 1 10 × 748.85 = 74.89 kg. Therefore, the underlayer mass of the quarry stone design is 74.89 kg. Calculating the underlayer thickness: r = 2 × 1 × ( 74.89 2323 ) 1 3 ≈ 0.648 m. Therefore, the underlayer thickness of the quarry stone design is 0.648 m. (B) Underlayer (mass and layer thickness) – Tetrapod Calculating the underlayer mass ¿ 1 10 × primary armourmass ¿ 1 10 × 186.55 = 18.66 kg. Therefore, the underlayer mass of the tetrapod design is 18.66 kg. Calculating the underlayer thickness: r = 2 × 1 × ( 18.66 2400 ) 1 3 ≈ 0.396 m. Therefore, the underlayer thickness of the tetrapod design is 0.396 m. d) The crest width can be considered as the distance between the seaside edge of the crest and the leeside edge. It offers a flat surface at the top of the breakwater and the magnitude of its width is generally determined by how it is intended to be constructed. (A) Crest width – Quarry stone Since the breakwater is meant to be constructed/maintained by machines and equipment on the crest. The crest width must consider the space required for these machines to operate. This includes the consideration of cranes, which can be used to dump the armour units, creating a heap or mound breakwater. The average width of a crane is around 3 m, therefore, to ensure secure movement when constructing the breakwater, a crest width of 4 m would be required. Hence, for the quarry stone breakwater it has been decided to implement a crest width of 4 m. (B) Crest width - Tetrapod For creating the tetrapod breakwater, the crest width isn’t necessarily determined by the type of constructed undergone to form the breakwater. This is due to the construction requiring a barge instead, meaning all the machines (trucks, bulldozers, cranes, etc) will run on the barges and so the work is done on the water next to the breakwater. This infers that the crest width can be any magnitude so to fulfill its optimum performance we can utilise the Hudson equation: B = mK ( M ρ ) 1 3 , where:  B is the crest width (m).  m is the number of units over the crest (making it 4 to ensure coverage of the crest).  K is the empirical shape factor (considering it is ‘cubic’, K = 1).  M is the primary armour mass (kg) – for this calculation the tetrapod mass was 186.55 kg.  ρ is the density of the concrete found as 2400 kg / m 3 . Hence, B = 4 × 1 × ( 186.55 2400 ) 1 3 ≈ 1.71 m. Therefore, the crest width of the tetrapod breakwater is 1.71 m. e) The construction method of a breakwater requires the use of personnel and machines and can be completed in many alternate forms. (A) Construction method – Quarry stone

The process essential to making a heap or mound breakwater out of quarry stone requires the use of excavators and bulldozers to prepare the construction of the breakwater. Next a crane can be used to drop the quarry stone armour units into the water, whilst stone-cutting machines are used to form more to be used later. This procedure continues until the mound emerges out of the water. (B) Construction method - Tetrapod The tetrapod breakwater will also use the design of a mound breakwater but will be constructed in a different form. With the assistance of barges, the construction can be done on the water to avoid the annoyance provided by the unique shape of tetrapod. With the barges moving on the water, all the required machines can work on top of it placing the tetrapods in their staggered pattern, interlocking with their adjacent armour units. After concrete can be layered on top, to hold the individual structures together. (A) Cross-Section – Quarry Stone Breakwater Figure 2 - Quarry Stone Breakwater Cross-Section with a rubble mound design at a scale 1cm:1m. Figure 2 displays the breakwater cross-section design for the quarry stone concept. Demonstrated by the dimensions having a 17.312 seabed width and a 3.328 m breakwater crest height, the design is a lot wider than it is tall due to the shallow water depth of the reservoir. Unique to the quarry stone design, the primary armour is a very thick layer and is 0.06 metres thicker than the core. This is due to the crest level not being required to cover a large distance due to the primary and underlayer thickness almost fulfilling the necessary height of the breakwater. The crest width was made 4 m purposefully to consider the use of large machines and vehicles in the construction of the breakwater. (B) Cross-Section – Tetrapod Breakwater

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Figure 3 - Tetrapod Breakwater Cross-Section with a rubble mound design at a scale 2cm:1m. Figure 3 displays the breakwater cross-section design for the tetrapod concept. Having a 2cm:1m scale instead of the 1cm:1m scale in figure 2 is due to the breakwater having a smaller magnitude, therefore covering less space. This is demonstrated by the smaller seabed width and breakwater crest height in figure 3 (being 13.6 m and 3.04 m respectively). In figure 3, the breakwater has a much larger core that makes up more than half of the structure’s thickness. This is due to the use of tetrapods and the effect of their unique properties. The crest width of the breakwater was also made narrower than usual due to the construction method having no influence on its value as all work was to be done from the water not on the structure. Section 3 – Calculating the Cost per Linear Metre of the Breakwater Designs Comparing the cost (per linear m) of the two alternative breakwater designs is possible through taking in account the prices for the materials. The price for the underlayer and core of both designs are worth $75/tonne. The primary armour layer of the quarry stone breakwater costs $145/tonne. Lastly, the concrete tetrapod primary armour layer is worth $290/tonne. However, to calculate the cost of each breakwater, the cross-sectional volume is required to find the unit price per metre. Firstly, it is necessary to find the total cross-sectional volume of the breakwaters using the area of a trapezium to find these values due to the similar shape that rubble mound breakwaters have. Especially since an assumption was made in the design briefing ‘that the depth of water immediately adjacent to both sides of the structure is equal and constant’. Adhering to this: total cross-sectional volume of the quarry stone breakwater, V ¿ h ( a + b 2 ) , where: - Cross-sectional volume ( m 3 ) - h is the breakwater crest height (m) - a is the crest width (m) - b is the seabed width (m) V = 3.328 × ( 4 + 17.312 2 ) ≈ 35.463 m 3 . Doing this again to find the total cross-sectional volume of the tetrapod breakwater:

V = 3.04 × ( 1.71 + 13.6 2 ) ≈ 23.271 m 3 . Next the cross-sectional volume of the sum of the underlayer and core must be found to determine its individual unit price, due to it being different to the cost of the primary armour layer. Hence using the formula for the area of a trapezium again, the cross-sectional volume of the core/underlayer section of the breakwaters can be found, however this time it is essential to consider the different crest heights and widths. For the quarry stone breakwater, the primary armour layer has a thickness of 1.37 m and so the crest height for just the underlayer/core will be 1.37 m shorter, making it (3.328 – 1.37 = 1.958 m) 1.958 m. The seabed width will also drop in size due to the primary armour layer, but considering it stretches beyond on both sides it decreases by double of what the crest height does ( 1.37 × 2 = 2.74 m ¿ . Hence the seabed width is 13.396 m (17.312 – 2.74 = 14.572 m). The crest width remains basically unchanged and due to the inability to approximate slight changes it will be assumed the crest width remains the same (4 m). Therefore, the cross-sectional volume, V = 1.958 × ( 4 + 14.572 2 ) ≈ 18.182 m 3 . Doing this again to find the underlayer/core cross-sectional volume of the tetrapod breakwater: Crest height = 3.04 – 0.85 = 2.19 m Seabed width = 13.6 − 0.85 × 2 = 11.9 m Crest width (remains unchanged) = 1.71 m Hence, the cross-sectional volume, V = 2.19 × ( 1.71 + 11.9 2 ) ≈ 14.903 m 3 . With the total cross-sectional volume and the underlayer/core cross-sectional volume, the sector of just the primary armour layer can be found. This is done by subtracting the underlayer/core section from the total, leaving only the cross-sectional volume of the primary armour layer. For the quarry stone breakwater this means that the primary armour cross-sectional volume is: V = 35.463 – 18.182 = 17.281 m 3 , and the tetrapod breakwater has a primary armour cross-sectional volume of: V = 23.271 – 14.903 = 8.368 m 3 . With all the volume measurements calculated, the last point of consideration before finding the price is the level of porosity (P). With this design it is assumed that 30% (or P = 0.3) of the space is taken by air and free or materials. Furthermore, it can be inferred that the materials will be considered for 70% (or P = 0.7) of the volume in each layer. This means each volume value will be multiplied by 0.7 to correctly account for the volume of the materials: - Underlayer/Core quarry stone breakwater volume ¿ 18.182 × 0.7 = 12.727 m 3 . - Primary armour quarry stone breakwater volume ¿ 17.281 × 0.7 = 12.097 m 3 . - Underlayer/Core tetrapod breakwater volume ¿ 14.903 × 0.7 = 10.432 m 3 . - Primary armour tetrapod breakwater volume ¿ 18.182 × 0.7 = 5.858 m 3 . Finally, the costs for each material can be found by multiplying the new-found volumes by its respective cost/tonne: - Quarry stone breakwater underlayer/core cost ¿ 12.727 × 75 ≈$ 954.53 / ¿ per linear metre - Quarry stone breakwater primary armour cost ¿ 12.097 × 145 ≈$ 1754.07 / ¿ per linear metre - Tetrapod breakwater underlayer/core cost ¿ 10.432 × 75 ≈ $ 782.40 / ¿ per linear metre - Tetrapod breakwater primary armour cost ¿ 5.858 × 290 ≈$ 1698.82 / ¿ per linear metre Therefore, the tetrapod breakwater is slightly cheaper per linear metre than the quarry stone breakwater.

Section 4 - Van der Meer’s Approach a) To determine whether the design wave is going to plunge, or surge it is determined by the Surf Similarity Parameter ( ζ z ) through comparing the surface slope of the wave to the bed slope in the surface zone. This is conducted using the formula: ζ z ≈ tanα √ ( 2 π H s ) ( gT z 2 ) , where: - α is the armour slope (1 on 2) - H s is the significant wave height (m) - T z is the zero-crossing wave period (s) which can be found with the formula: T z = 0.71 T P = 0.71 × 5 = 3.55 s. Hence, ζ z ≈ 2 √ ( 2 π× 1.5 ) ( 9.81 × 3.55 2 ) ≈ 7.244 . Since the surf similarity parameter ζ z > 3.5 , it means that the waves will tend to surge on the structure. b) Using the Van der Meer approach, it is possible to find the primary armour sizes for the quarry stone design based on different storm durations. It is also feasible to find these magnitudes based on different cases such as considering there is no damage or even if there is some degree of breakwater damage. This can all be done using the zero-crossing wave period ( T z ), significant wave height ( H s ) surf similarity parameter ζ ( ¿¿ z ) ¿ . Assuming the core is permeable due to the quarry stone breakwater utilising a rubble mound design, which commonly uses them, the stability number ( N s ) can be found. However, first is necessary to find the number of waves during the duration of wave attack (N) and the unit damage level (S). N = duration of wave attack (storm duration) ÷T z There are three different storm durations, being 4, 8 and 12 hours. So, when the storm duration is: - 4 hours (or 14400 seconds) → N = 14400 ÷ 3.55 ≈ 4056.34 waves - 8 hours (or 28800 seconds) → N = 28800 ÷ 3.55 ≈ 8112.68 waves - 12 hours (or 43200 seconds) → N = 43200 ÷ 3.55 ≈ 12169.01 waves S can be approximated with the data calculated by Van der Meer in table 2: Table 2 - Provides the magnitude of S based on the level of the damage to the breakwater and its slope. From table 2 for this specific quarry stone breakwater, it is essential to refer to the top row since the breakwater slope in said design is 2. Using this data, we can determine what S is for a breakwater with no damage and for one with a degree of damage. For no damage it would be viable to consider S = 1 as it should be less than S = 2 (start of damage) but also a positive value. A breakwater with a

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degree of damage should be between the start of damage and failure columns in table 2. It would be wise for approximation purposes to take the intermediate value since the severity of damage is not indicated and therefore, S = 5. With all the values necessary, the stability number ( N s ¿ can be found. There are three different permeability core, empirical equations all with different conditions for use. For this certain quarry stone breakwater, according to the surf similarity parameter the waves tend to surge and following the conditions of the permeable core equations the design matches one of them: N s = 1.65 √ cotα ( S √ N ) 0.17 ζ z 0.1 , where α < 3 for cot ¿ ζ z > 2.5 ¿ 3.5 ¿ . 1. N s for no damage to breakwater: - Considering N value for a storm duration of 4hrs → N s = 1.65 × √ 2 × ( 2 √ 4056.34 ) 0.17 × 7.244 0.1 ≈ 1.579 . - Considering N value for a storm duration of 8hrs → N s = 1.65 × √ 2 × ( 2 √ 8112.68 ) 0.17 × 7.244 0.1 ≈ 1.489 . - Considering N value for a storm duration of 12hrs → N s = 1.65 × √ 2 × ( 2 √ 12169.01 ) 0.17 × 7.244 0.1 ≈ 1.439 . 2. N s for a degree of damage to the breakwater: - Considering N value for a storm duration of 4hrs → N s = 1.65 × √ 2 × ( 5 √ 4056.34 ) 0.17 × 7.244 0.1 ≈ 1.846 . - Considering N value for a storm duration of 8hrs → N s = 1.65 × √ 2 × ( 5 √ 8112.68 ) 0.17 × 7.244 0.1 ≈ 1.7 40 . - Considering N value for a storm duration of 12hrs → N s = 1.65 × √ 2 × ( 5 √ 12169.01 ) 0.17 × 7.244 0.1 ≈ 1.681 . Next, by rearranging the Hudson Stability equation ( N s = H s Δ D 50 ¿ , the nominal diameter ( D 50 ) can be found with D 50 = H s ∆ N s , where ∆ is the relative mass density, which was found in Q2. 1. D 50 for no damage to breakwater: - Considering N s value for a storm duration of 4hrs → D 50 = 1.5 1.323 × 1.579 ≈ 0.718 m. - Considering N s value for a storm duration of 8hrs → D 50 = 1.5 1.323 × 1.489 ≈ 0.761 m. - Considering N s value for a storm duration of 12hrs → D 50 = 1.5 1.323 × 1.439 ≈ 0.788 m. 2. D 50 for a degree of damage to breakwater:

- Considering N s value for a storm duration of 4hrs →D 50 = 1.5 1.323 × 1.846 ≈ 0.614 m. - Considering N s value for a storm duration of 8hrs → D 50 = 1.5 1.323 × 1.740 ≈ 0.652 m. - Considering N s value for a storm duration of 12hrs → D 50 = 1.5 1.323 × 1.681 ≈ 0.674 m. - Finally, with these results the mass of the primary armour in the quarry stone breakwater can be found through rearranging the nominal armour diameter equation ( D 50 = [ M 50 ρ ] 1 3 ). Hence the median value of the armour mass distribution, M 50 = ρ D 50 3 . Therefore, through using this equation the mass of the breakwater when: 1. There is no damage to the breakwater: - And considering D 50 for a storm duration of 4hrs → M 50 = 2323 × 0.718 3 ≈ 859.85 kg. - And considering D 50 for a storm duration of 8hrs → M 50 = 2323 × 0.761 3 ≈ 1023.77 kg. - And considering D 50 for a storm duration of 12hrs → M 50 = 2323 × 0.788 3 ≈ 1136.65 kg. 2. There is a degree of damage to the breakwater: - And considering D 50 for a storm duration of 4hrs → M 50 = 2323 × 0.614 3 ≈ 537.72 kg. - And considering D 50 for a storm duration of 8hrs → M 50 = 2323 × 0.652 3 ≈ 643.86 kg. - And considering D 50 for a storm duration of 12hrs → M 50 = 2323 × 0.674 3 ≈ 711.26 kg. Therefore, the revised Primary Armour (Quarry Stone) sizes for no damage, referring to 4-, 8- and 12- hour storm durations are 859.85 kg, 1023.77 kg and 1136.65 kg in respective order. The sizes for when there is a degree of damage and there are 4-, 8- and 12-hour storm durations are 537.72 kg, 643.86 kg and 711.26 kg in respective order. Section 5 – Consideration of Increased Water Level in the Reservoir a) To incorporate the future water level of the reservoir being 2.5 m (an extra 1 m higher than its original state) with the same wave climate, a new wave height and period must be selected for the preliminary breakwater design to account for these future changes. Using figure 1 again, it is possible to calculate these new values and determine where the waves will be broken or unbroken at the face of the structure. Using the same method as in Q1, with figure 1 the wave height can be identified by the equation: H b d s = 0.9, where H b = 0.9 ×d s . Since the surge of the wave also must be considered, d s = 2.5 + 0.1 = 2.6 m, furthermore: H b = 0.9 × 2.6 = 2.34 m. However, due to the water rising by 1 m it also safe to assume that the significant wave height ( H s ¿ value has risen by 1 m as well making its new value 2.5 m. (1.5 m + 1 m = 2.5 m) Therefore, in these conditions the H b (being 2.34 m) is smaller than H s ( being 2.5 m ) , inferring that the design wave height can be considered the height of H b , making it 2.34 m. This also confirms for this breakwater design the waves are breaking at the face of the structure.

Finding the wave period also requires the same method used in Q1, through referring to figure 1 it can be identified: H b d s = m× d s ( gT 2 ) , which can be rearranged to make T the subject as: T = √ md s 2 H b g = √ 0.01 × 2.6 2 2.34 × 9.81 ≈ 0.054 seconds. Therefore, the wave period for these new conditions is 0.054 seconds. b) Based on the new information, the required mass of the quarry stone primary armour can be found with the Hudson equation: M = ρ H 3 K D ∆ 3 cotα , where the wave height will be the breaking wave height and all the other values will remain the same as in Q2 for the quarry stone breakwater. Hence, M = 2323 × 2.34 3 2 × 1.323 3 × 2 ≈ 3213.34 kg . Therefore, the required mass of the primary armour layer in the quarry stone breakwater with the water level risen by 1 m is 3213.34 kg. Comparing this armour size to the other results in Q2 and Q4, due to the future rise in water level, the required armour size is a lot larger and quantitatively around 4-5 times the size of the other results. Deciding whether to consider the future water level rise into the conceptualisation of the breakwater design for the Australian Water-Skiing Championships in 2024 is unnecessary. This is because for at least 10 years the breakwater will function optimally, making it not worth the time and money required to account for the much larger design if these future changes were to be considered in this project. Conclusion The preliminary breakwater design has been drawn into a cross-section through calculating all the variables necessary to make a conceptualisation that is to scale. Comparing the calculations with two different approaches through the Hudson and Van der Meer equations confirms a successful investigation as both gave similar results. Given the number of assumptions made clearly outlined in the methodology, it is quite surprising that the results were able to remain consistent, since assumptions in calculations can lead to wrong answers caused by too many approximations. In order to improve the breakwater design, it would be beneficial to utilise more field research to increase the accuracy of the results and to also decrease the number of assumptions made in the calculations. Methods utilised to determine the cost of materials used on the breakwater could also be made easier by investigating the length that the structure stretches to. Allowing the volume to be found and so then the price per linear metre to be calculated directly. In conclusion, the preliminary breakwater design was successfully conceptualised through a cross-section and calculated through investigating the waves at the reservoir, materials used to build the breakwater, the cost of these materials and future changes to the breakwater and reservoir. References Mound breakwater: Types, construction and protection (2021) The Constructor . Available at: https://theconstructor.org/water-resources/mound-breakwater-types-construction-and- protection/559854/#:~:text=Heap%20or%20Mound%20Breakwater,-It%20is %20a&text=This%20is%20the%20simplest%20type,waves%20regulates%20its %20side%20slopes. (Accessed: April 8, 2023). Present practices in design of rubblemound breakwaters for ... - INPRESSCO (2018) Present Practices in Design of Rubblemound Breakwaters for Coastal Harbours-A Review . International Journal of Current Engineering and Technology. Available at: https://inpressco.com/wp-content/uploads/2018/06/Paper30744-752.pdf (Accessed: April 4, 2023).

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