The Experiment on the Coastal Engineering to Analyse the Wave Behaviour and Linear Theory - Lab Report Example

Contents Breakwater Design 12 The typical design of a breakwater must consider of logistical factors, like the depth of water that finds out quantityof materials. A basic part of the breakwater is a bed of armour units on the slope that faces the prevailing waves. In one structure predicted to have strong armour layer to be resistant from damaging waves. Usually, the different degrees of interlocking and resistance to displacement by waves created from concrete blocks with different types of shape. 12 The Hudson equation is used to find the size of the blocks i.e. 12 where ρm = density of material for (rock = 2650 kg m–3) 12 (concrete = 2400 or 2250 kg m–3) 12 ρw = density of seawater ( = 1025 kg m–3) 12 Hs = design wave height (usually taken as Hs) 13 KD = non-dimensional constant for armour units 13 α = angle of structure slope facing the waves 13 The advantage of rubble mound structures is: 13 1)Failure of the amour cover layer is not typically sudden. 13 2)The structure continues to function during the storm. 13 3)The damage can be repaired after the storm. 13 The slope facing waves should never be steeper than 1 (v) in 1.5 (h). 13 The armour layer should extend at least 2 times the design wave height below MLW. 13 The secondary armour layers, if the armour unit mass is M, first ‘filter’ layer beneath should be 1/10–1/15 × M and second under layer ~1/200 × M. 13 A usual breakwater: 13 13 Data 13 Design wind data 13 19 19 19 19 19 19 Armour Units 19 20 Figure: Armour units (panoramio.com, 2012-04-13) 20 Armour unit refers to large quarried stone or specially shaped concrete block used as primary protection against wave action. They are of variety of shapes and sizes. The thickness is always twice the diameter of concrete armour unit for the tetra pod layers Concrete. 20 21 21 The concrete density is: 21 22 Because the slope is 1:1.5 it would be preferred to use a denser concrete where, making the required mass would be 6.3 tons. 22 Section B 22 Section B is more exposed than A in general. 22 22 Slope of breakwater 23 The max wave height at minimum tide before breaking is 23 MLWS: with this tide maximum wave height before breaking is 23 At MLWS tide the wave height has approximately reached the maximum wave height, before breaking. 23 All wave height from this tide on is taken as 4.25 m and there is no need for further calculations. 23 23 Armour Units 24 24 Introduction The experiment on the coastal engineering was carried out in the hydraulics laboratory for approximately two hours. This experiment consisted of two parts. Part one was linear wave theory and part two was breakwater design. The venue of the experiment was Sopwith building Waves are created when wind blows on top of the sea and the bottom layer receives frictional drag from the surface of the sea which exerts frictional drag to the next wind layer above it. This process continues in all the wind layers. The coastal zone is very important to the community around it. For the community to survive, the engineers play a big role in protecting this zone against flooding, erosion and destruction of property by the ocean waves and tides. The laboratory work is important in that to avoid all this natural disasters. Laboratory report To analyse the wave behaviour and linear theory, the observation of different sets of waves was done. The waves had the periods of 1.0s 1.5sand 2.0s. The speed, length and height of the waves facilitated calculation of the theoretical values of the wavelength The measurements lead to commendation on how the waves acted on the coast and how they were reflected on the vertical wall. The waves that are reflected on the vertical surface had no horizontal movement and are referred to as standing waves. A rubble mound breakwater was created to make the wave to move over it Smaller waves with period 1.0s, were created to come to the conclusion about how they affect the model structure. This observation ended when the rubble mound breakwater finally failed. 1. Waves The wave height of a surface wave is the difference between the elevations of a crest (the highest point of the wave) and a neighbouring trough (the lowest point of the wave) as it is shown at the figure below. (Dr Alan Dykes, 2011). The stronger the wind for a long time, the higher the height of the wave thus the wave size. The stronger the wind, the stronger the wave’s height but constant H = height (m) a = amplitude = H/2 L = wavelength (m) T = period (s) f = frequency = 1/T (s–1) (number per second) Linear wave theory The speed of the wave, or its celerity, C, is the distance travelled by a crest per unit time given by the formula below. c = L / T (m s–1) And c = gT .tanh 2πd Where d= is the depth in meters T is the wave period in seconds. Wave number: k = 2π / L Wave frequency: ω = 2π / T Therefore celerity, c = (g/ω) tanh (kd) Summary of the waves The deep water formula: d/L0 > 0.5 è c0 = (gL0 / 2π)½ The intermediate or transitional depth formula: 0.04 < d/L < 0.5 è c = gT .tanh 2πd The shallow water formula: d/L < 0.04 è c = (gd)½ and this is independent of the wavelength. For all the depths formula: è c = L/T As the waves move into the shallow water, their period must stay the same, the speed will be reduced and the wavelength will reduce too. (Dr Alan Dykes,2011) Data recorded The data recorded during the experiment and the results from the calculations are shown in the table below, when the water depth is 3.0 meters. Set-up Wave speed measurements Wavelength Measured wave length Shallow or intermediate Measure wave Wave period, T Distance, x Time for wave to travel distance Wave speed (celerity), c = x/t C = L/T therefore L = c x T d/L H (s) (m) (s) (m) (m) ratio (m) 1.0 7.55 5.59 1.29 1.25 1.25 2.4 0.055 1.5 7.55 4.73 1.515 1.477 2.21 2.03 0.0775 2.0 7.55 4.75 1.505 1.45 2.90 2.07 0.0715 This graph is used to approximate the ratios in the following Theory Co = gT/2π Lo = Co x T from graph d/L from graph Theoretical L for interim. depth in flume? Theoretical c from (m) ratio ratio (m) 1.56 1.56 0.192 0.218 1.376 1.376 2.34 3.51 0.085 0.127 2.362 1.575 3.12 6.24 0.048 0.092 3.261 1.631 2. Energy dissipation A vertical wall was placed at the coastline to observe how the waves act when they strike on the wall. 3. Rubble mound breakwaters This part of the experiment involved setting up of small regular waves with wave period T=1.0s to observe their effect on the rubble mound breakwater. The wave height increased gradually until failure occurred. The Hudson equation facilitated the estimation of the mass of the armour. The scale of the model was 1:100. 60mm of the model are equal to 6.0 meters of the prototype and this could be easily found because the scale was 1:100. At 80mm much more than 5% of the model failed and as a result this was the design height. The stones which fail were 10 and their weight was 580 grams. The breakwater properties are the following: Slope is 1(v) against 0.84(h) So the minimum mass of the armour unit required is given from the Hudson Equation: And that is equal to 43.3 tonnes. 4. Breaking waves The waves reached the shallow in different ways. It was observed that waves were with different wave periods. Discussion Comparing columns 4 and 5, columns 3 and 13 and columns 4 or 5 and 12. The linear wave theory proves to be true from the notification from experimental results. The small difference may be due to parallax error in reading the results, vibrations, friction etc. The steepness of the coast and steepness of the waves affects the braking waves. This experiment enabled realization of the importance of breakwater model experiments for coastal structures and the designation of proper breakwater. Breakwater Design The typical design of a breakwater must consider of logistical factors, like the depth of water that finds out quantity of materials. A basic part of the breakwater is a bed of armour units on the slope that faces the prevailing waves. In one structure predicted to have strong armour layer to be resistant from damaging waves. Usually, the different degrees of interlocking and resistance to displacement by waves created from concrete blocks with different types of shape. The Hudson equation is used to find the size of the blocks i.e. where ρm = density of material for (rock = 2650 kg m–3) (concrete = 2400 or 2250 kg m–3) ρw = density of seawater ( = 1025 kg m–3) Hs = design wave height (usually taken as Hs) KD = non-dimensional constant for armour units α = angle of structure slope facing the waves The advantage of rubble mound structures is: 1) Failure of the amour cover layer is not typically sudden. 2) The structure continues to function during the storm. 3) The damage can be repaired after the storm. The slope facing waves should never be steeper than 1 (v) in 1.5 (h). The armour layer should extend at least 2 times the design wave height below MLW. The secondary armour layers, if the armour unit mass is M, first ‘filter’ layer beneath should be 1/10–1/15 × M and second under layer ~1/200 × M. A usual breakwater: Data Design wind data Wind direction Wind speed (m/s) Duration (h) Fetch length (km) East 16 8 200 ESE 18 8 100 SE 20 6 100 SSE 22 6 100 South 22 6 100 Tidal data HAT 5.1 m above chart datum MHWS 4.9 m above chart datum MHWN 3.7 m above chart datum MLWN 1.3 m above chart datum MLWS 0.4 m above chart datum LAT 0.1 m below chart datum Waves on site To determine the incoming waves from storm surges, the wind chart below is used. Wind direction Hs from table (m) Ts from table (s) Duration from graph (h) Fetch-ltd. East 3.2 7.7 12 Duration-limited waves ESE 3.25 7.2 6.5 Fully arisen sea SE 3.75 7.7 6 Fully arisen sea SSE 4.25 8.1 5.7 Fully arisen sea South 4.25 8.1 5.7 Fully arisen sea Water depths Map of the coast showing different depths and distances The table below shows the different depths with the tides along the three marked lines on the above Map Depths from min to max Red zone (m) Blue zone (m) Green zone (m) 1 1.9 3.9 5.9 2 2.4 4.4 6.4 3 3.3 5.3 7.3 4 5.7 7.7 9.7 5 6.9 8.9 10.9 6 7.1 9.1 11.1 Section A Top Level of Breakwater The possibility of the highest wave shows from the top level breakwater. In coastal engineering the design is taken as the largest wave height=4.25m. Assume the top level is 9.40m. Slope of Breakwater The slope should be between 1:2 and 1:1.5. The breakwater slope should extend twice the height of the waves .The wave height is 0.78d Ats Armour Units Figure: Armour units (panoramio.com, 2012-04-13) Armour unit refers to large quarried stone or specially shaped concrete block used as primary protection against wave action. They are of variety of shapes and sizes. The thickness is always twice the diameter of concrete armour unit for the tetra pod layers Concrete. The Hudson equation and the above table: The concrete density is: Because the slope is 1:1.5 it would be preferred to use a denser concrete where, making the required mass would be 6.3 tons. Section B Section B is more exposed than A in general. d = 10.1 m H = 4.25 m Assume Breakwater Height as 12.4 m Slope of breakwater The max wave height at minimum tide before breaking is MLWS: with this tide maximum wave height before breaking is At MLWS tide the wave height has approximately reached the maximum wave height, before breaking. All wave height from this tide on is taken as 4.25 m and there is no need for further calculations. This section has a slope of 1:1.5 hence all the structural requirements are Armour Units For section B two layers of armour concrete tetra pod blocks will be used as well. Section B is the head of the breakwater and this is why the design parameters for the armour unit minimum mass change. The concrete tetra pod blocks need to have a mass of at least 7.9 tons. Discussion-Conclusion Understanding of the sediment transfer is vital for coastal engineers. This facilitates production of required equipment to protect the coast and the community around this zone. This enhances analysis of different masses of flow to determine the sediment transfer characteristics. The experimental work on the coastal engineering enabled the students to understand the wave behaviour and apply the theoretical knowledge learned in class work. References 1. Coastal portal. (2008). Definition of Armour unit. Available: http://www.coastalwiki.org/coastalwiki/Armour_unit. Last accessed 13 april 2012. 2. scubageek.com. (1997). Water Wave Celerity . Available: http://scubageek.com/articles/wwwceler.html. Last accessed 13 april 3. Robert M. Sorensen. (1993). Waves. In: John Wiley & Sons Basic Wave Mechanics for Coastal and Ocean Engineer. Newyork: Longhorn. p78-80. 4. Wikipedia. (2010). Waves. Available: http://en.wikipedia.org/wiki/Wave_height. Last accessed 13 april 2012. 5. Dr Alan Dykes ( lecture notes) Read More