Coastal engineering assignment requiring MATLAB

Coastal Engineering and Modelling – 6110ENG

Assignment 1- Simple Coastal Models Trimester 1, 2019

Due date: 11 PM Wednesday, May 7, 2019, Week 10.

Submission Instructions:

1. Work individually 2. Complete all tasks as instructed with the assignment question sheet 3. Submit both the report and MATLAB script file electronically to the “Submission

Dropbox_Simple Coastal Models Assignment, Due on May 7, 2019” link on

Learning@Griffith – “Assessment”

Question 1: (40 marks)

A submerged pressure sensor can serve as a wave gauge if it is adequately sensitive to detect

the wave induced dynamic pressure. There is a swell wave with the deep-water characteristics

(period T0 and wave height H0 measured by an offshore buoy) perpendicularly propagating

toward a straight shoreline. At the coast near the shoreline, a pressure sensor is installed as

shown in the Figure below. For the progressive swell wave, the minimum and maximum

pressures (Pmin and Pmax at the Sensor are recorded as well. (The density of seawater to be 1026

kg/m3). The wave data of 5 storm events have been included in the Table below. Develop a

simple coastal model to (i) estimate the swell wave height at the coast using the measured data

and (ii) estimate the Shoaling Coefficient for all events. Assume the linear wave theory is valid.

Sensor 1

Deep water buoy record Pressure senor at the Coast

H0 (m) T0 (s) Pmin ( kPa) Pmax ( kPa)

1 3.5 25 76.4 126.7

2 4.1 15 78.2 122.2

3 2.9 18 80.6 119.2

4 3.8 12 82.2 118.2

5 7.1 7 80.6 120.6

Numerical solutions (18 marks)

Develop a simple model using MATLAB to:

(i) Calculate the wave characteristics (i.e. wave height, wave length, wave number, wave

celerity) at the coast by solving the Dispersion Relation Equation numerically using

fzero( ) function in MATLAB with relevant linear wave equations;

(ii) Calculate the Shoaling Coefficient using two methods: (i) the linear wave theory and

(ii) the recorded data, for all 5 events; and compare the results from both methods for

further uncertainty discussion. Generate a figure to show the relationship between the

relative water depth and the shoaling coefficient;

(iii) Generate figures to show the surface wave elevations timeseries (i) offshore and (ii) at

the coast for Event 1 over 4 wave periods, and

(iv) Generate figures to present the vertical profile (from bottom to the surface) of the

maximum water particle horizontal and vertical velocities at the location of the Sensor

for Event 5 (for the discussion of the relationship between the maximum horizontal and

vertical velocities).

Report (24 marks)

Complete a report that address and solves all tasks listed above. It must include:

 Introduction: Introduce the problem and explain your methodology, i.e. problem

formulation including all relevant equations and numerical method used

 Results and discussion: Display the data in a clear and appropriate manner, i.e. all figure

axes and table columns must be properly labelled with the correct units, captions and

brief explanation and discussion are required for all figures.

 Conclusion: A brief analysis that summarises the data and draws some conclusions.

Question 2: (60 marks)

The long-term wave data (recorded at a certain location over a long period of time) provides the

probability or number of occurrence of sea states in a specified ocean area. Typically, a minimum

return period (T) of 100 years is required for design conditions. If it is accepted by the coastal

engineering design guidelines A minimum return period of 50 years may be specially considered.

Statistical distributions are used as a tool to generate recurrence interval and estimate specific design

wave characteristics. The procedure is summarised as:

1. Collect a large available wave data set (thumb rule: at least T/2 years of data)

2. Calculate the probability of exceeding a given event magnitude,

𝑃{𝑋 ≥ 𝑥𝑛} = No of 𝑋 ≥ 𝑥𝑛 Total No of 𝑋

Then the cumulative probability density function

𝐹(𝑥𝑛) = 𝑃{𝑋 < 𝑥𝑛} = No of 𝑋 < 𝑥𝑛 Total No of 𝑋

= 1 − 𝑃{𝑋 ≥ 𝑥𝑛}

3. The return interval for event 𝑥𝑛 is

𝑇(𝑥𝑛) = 1

1 − 𝐹(𝑥𝑛)

4. Plot 𝑥𝑛 versus log 𝑇(𝑥𝑛), and determine the return the interval for any given 𝑥𝑛

A coastal engineering firm, ABC Coastal Solution, has bid the project to design an impermeable rock

groyne structure at the Coast GC. The construction site is identified in Figure 1, where the water depth

is 5.7 m and there is a long historical wave monitoring data set from 1987 to 2013 (see the attached

file). 2. The impermeable rock groyne structure has a slope of 1 in 2.5 and is subjected to a design

wave condition (H2%) estimated from the long-term monitoring data. Using the Hudson formula,

estimate the weight of uniform-sized, rough angular armour stone (s = 2650kg/m 3) required for the

trunk and the head of the structure.

Numerical solutions (24 marks)

Develop a simple model to analyse long term waves using MATLAB and the provided data set:

(1) Generate a scatter diagram and the histogram of the monitoring wave data set. Show the maximum

wave of each year.

(2) Calculate and show the cumulative probability density function of wave events

(3) Calculate and show the probability of exceeding of the wave heights and compare it with Rayleigh

Distribution

(4) Show the relationship between the given wave heights and their correspondent return periods up

to 100 years

(5) Estimate the wave heights for the return period of 50 years and 100 years.

(6) Complete the structure design using the predicted design wave conditions (with 50 years

return period) and the given structure conditions.

Figure 1: The map of Coast GC and the construction site.

Report (36 marks)

Complete a report that address and solves all tasks listed above. It must include:

 Introduction: Introduce the problem and explain your methodology, i.e. problem

formulation including all relevant equations and numerical method used

 Results and discussion: Display the data and results in a clear and appropriate manner,

i.e. all figure axes and table columns must be properly labelled with the correct units,

captions and brief explanation and discussion are required for all figures. Interpret

and describe the significance of your finding from the presented results. The limitation

of the method must be discussed as well.

 Conclusion: A brief analysis that summarises the data and draws some conclusions.

Construction site