The impermeable rock gryone structure to be constructed at the Coast GC is a structure that will consist of steel reinforcement and cast in place concrete – the standard design of a majority of civil and structural engineering. The project is to be undertaken at a construction site identified as shown in Figure 1. The location of the project has no historical wave monitoring data; however, the bathymetry data and the historical wind data for the area are available and were useful in the development of the design. Table 1 presents the 50 year ARI design wind in the research domain for the area. The design project applied DHI MIKE 21 SW model to predict the design wave conditions using the provided design wind conditions.
Model and Design Formula
The design was done through spectral wave model analysis using relevant parameters as indicated in the ‘Key Model Parameters’ section. The design development involved complete simulations of the area using design wind conditions and wave output parameters. This was followed by an in-depth analysis wave data of three key design aspects: (1) the developed wave height/direction and period distributions, (2) the wave characteristics at the construction site, and (3) the developed wave spectral parameter at the construction site. The results section of the report presents the critical design wave and wave characteristics.
Key Model Parameters
Figure 1 below is satellite map showing the location of the project – where the construction will take place. Next to the figure are the Bathymetry data (in meters) that was used.Other important design data/parameters utilized in the project are the 50 year ARI design wind in th research domain. The data is represented in Table 1 below.
Table 1: 50 Year ARI Design Winds at the Coast GC.
|
Wind direction
|
N
|
NW
|
S
|
SE
|
|
|
|
|
|
|
|
Wind speed (m/s)
|
20.2
|
22.1
|
20.6
|
28.8
|
|
|
|
|
|
|
Accurate prediction of design waves is essential when determining design data for coastal structures (Torum & Gudmestad, 2012). The safety of structures, as well as the possibility of developing an economic design, relies above all on the reliability and accuracy of the underlying design data.
The following data information was used in design development:
- Bathymetry data, from the pre-generated file of “CoastGC_Bathy.mes
The domain has Northern, Southern and Eastern open boundaries. “Lateral boundary” applies to all of them. The coastal structure toes is at (Easting 550000, Northing 6890000) with a water depth of 8.80 m.
- The MIKE 21 SW parameters applied include the following:
- Time: No of time steps 100, Time step interval: 1800 s
- Basic equations: Fully spectral formulation and Instationary formulation
- Spectral discretization: 25 frequencies and 16 directions
- No water level and current variations
- Diffraction – no diffraction
- Energy transfer - Include quadruplet wave interaction
- Wave breaking – Specified gamma, constant, value = 0.8
- Bottom friction - D50 sand size is 0.0002 m
- White capping – no white capping
- Initial condition - default JONSWAP fetch growth expression
Modeling part of the design gave:
|
Wind Direction
|
N
|
NW
|
S
|
SE
|
|
Wind speed
|
20.2
|
22.1
|
20.6
|
28.8
|
|
Signi.wave height
|
4.523
|
4.368
|
4.07
|
4.79
|
|
Peak Wave period
|
12.55
|
11.169
|
11.96
|
14.29
|
Methodology and formulas
The following were used in a pre-generated ‘CoastGC_bathy.mesh” file opened in MIKE 21 SW and the simulation run:
- Time up, 100 steps and 1800 sec.
- Given wind speeds and directions,
- Boundary conditions as lateral boundary.
- Point series,
- Area series
- Spectral series
The spectral wave model was established using the MIKE 21 SW. the application is a 3rd generation spectral wind wave model, a development of DHI. The model was applied in the simulation of the growth, decay and transformation of wind generated waves and swells with the CoastGC, construction site. Both a full spectral and directional decoupled parametric formulations were included in this analysis.
The figures below show the simulation results from MIKE 21 SW model based on the key model parameters specified for the project:
Figure 1. Spectral Wave Model![]()
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Formula and solution:
Design wave height,
Wave height at the breakwater,
Where-
Hudsons Formula
Stability number,
Calculations:
From the result maximum height is for the south-east direction-design height
Therefore,
Significant height,
Peak wave period,
For:
Break criteria,
Water depth breakwater,
Slope, tan
Density of BW,
The density of water
Find
For finding this, we need value:
We can find it on the Raleigh distribution chart given below:
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Conclusion
The models in MIKE21 are presented in a wave action density. Two governing equations are used to compute the full spectral formulation and the directional decoupled parametric formulation.
The wave height, period distributions, wave direction and wave spectral parameter over the CoastGC were an integration to investigate the coastal wave process associated with the area. The MIKE 21 SW by DHI was used. The simulation coupled a spectral wave model with other wave parameters as shown to simulate the wave characteristics.
In addition, the model simulated decay, growth and the transformation of the waves simulated by the wind. The analysis used both the directionally-decoupled and quasi-stationary formulations. All the components used in the model took place at each time step. The MIKE 21 SW zipped files have a detailed description of the formulations and the coupled model spectrums.
The MIKE 21 SW results gave the results which were used to calculate stone weight and trunk. Also, the wave wind energy is highest away from the ocean and low at the bed level
References
Torum, A., & Gudmestad, O. T. (2012). Water wave kinematics (Vol. 178). Springer Science & Business Media.
Lin, P., 2014. Numerical modeling of water waves. CRC Press
