effect of submerged breakwater configuration on … · 2015-10-15 · the results from this study...

EXPERIMENTAL STUDY ON THE EFFECT OF SUBMERGED BREAKWATER CONFIGURATION ON LONG WAVE RUN-UP REDUCTION

A THESIS SUBMITTED TO THE GRADUATE DIVISION OF THE UNIVERSITY OF HAWAII AT MANOA IN PARTIAL FULFILLMENT OF

THE REQUIREMENTS FOR THE DEGREE OF

MASTER OF SCIENCE

IN

CIVIL ENGINEERING

December 2014

By

Tony K.C. Shing

Thesis Committee:

Michelle H. Teng, Chairperson

Oceana Francis

Ian N. Robertson

1

Abstract

Experimental study was carried out to observe and quantify the effects that a submerged

breakwater has on long wave run-up reduction. As shown in the past, long wave run-up, or

tsunami can be very devastating. In 2011, the tsunami in Japan resulted in over 300 billion

dollars of damages along with several thousand lives. A recent finding of coral and ocean

sediments found in a sinkhole in Kauai suggest that this catastrophic event could happen in

Hawaii. The focus of this thesis study is to find the optimal breakwater length for run-up

reduction and examine the effects that a breakwater’s geometry has on run-up reduction, aiming

at seeking specific configurations and designs of submerged breakwater that may be effective in

reducing long wave run-up. This included experimental test on waves of different amplitude (up

to 10 different amplitude) propagating over breakwater models of different material

(rigid/impermeable/smooth surface vs. flexible/porous/rough surface), length, spacing, and

geometry, and running-up onto artificial beach of different slopes. In addition, the experimental

results were compared with a previous numerical study done by Mohandie (2008) and Mohandie

and Teng (2012). In their numerical study, it was found that when the length of a submerged

rectangular breakwater is twice the wavelength of the generated long wave, the maximum run-up

reduction rate was achieved. This numerical result had not been examined and validated in an

experiment before this thesis study.

In the present thesis study, it was found that foam/flexible breakwater material provided a

better run-up reduction than plastic/rigid material. For the effect of the geometry of the

breakwater, a triangular saw-tooth geometry provided better run-up reduction than a circular

speed bump geometry. Both triangular and circular models provided better run-up reduction

2

than a flat rectangular model. For the effect of breakwater length, the experimental results

generally follow the same trend as the numerical simulations done by Mohandie and Teng (2012).

The results showed a trend of increasing run-up reduction until a certain point before decreasing

as the model length increases. The point at which the run-up reduction decreases varied in the

experimental results and ranged from 1.25-1.9 wavelengths. In the 5 degree beach slope test,

two rectangular breakwater models with a spacing in-between compared to a breakwater models

of equal length without the spacing showed no significant difference in run-up reduction.

However, in the 10 degree beach slope test, the results were mixed. The rigid rectangular model

had a better run-up reduction for the breakwater model with spacing whereas the flexible

rectangular model had a better run-up reduction for the breakwater without spacing. This issue

may require further investigation.

The results from this study may be useful in future design of submerged breakwaters for

reducing long wave run-up. Specifically, we recommend breakwaters with a saw-tooth geometry,

or of flexible/porous material with a rough surface. For the breakwater length, it should be

comparable to the wavelength, if practically possible in near shore regions.

3

Acknowledgment

I would like to thank Professor Michelle H. Teng, for her dedication and support

throughout the years. Without her, I would not have started my master studies, much less finish

it. I am grateful for Professor Oceana Francis and Ian N. Robertson for their advice and

willingness to help. I want to thank the CEE department for offering me teaching assistantship

and scholarships during my graduate studies. Besides the financial support, the teaching

assistantship was a great experience. I am thankful for Thi Hong Vo for helping me along the

way and for volunteering her time to help me with the experiments. I am thankful for Ame

Arakaki for all her help and for her assistance with the models. I would also like to thank our

summer interns Kap’a Akau and Selena Torres for their valuable input in this master thesis. I

would like to thank Board of Water Supply and my supervisors Ann Wong and Lyann Okada for

being supportive and flexible throughout my master’s studies. Lastly, I would like to thank my

family and friends for always being there.

4

Table of Contents

Abstract ........................................................................................................................................... 2

Acknowledgment ........................................................................................................................ 4

CHAPTER 1 INTRODUCTION ........................................................................................... 13

1.1 Technical Background.................................................................................................... 13

1.2 Literature Review ........................................................................................................... 14

1.3 Objective of Present Study ............................................................................................. 15

CHAPTER 2 THEORY, GOVERNING EQUATIONS AND EXISTING NUMERICAL

RESULTS 16

2.1 Governing Equations for Long Wave Propagation ........................................................ 16

2.2 Governing Equation for Long Wave Run Up ................................................................ 17

2.3 A Solitary Wave as the Initial Wave .............................................................................. 18

2.4 Existing Numerical Results ............................................................................................ 19

CHAPTER 3 EXPERIMENTAL DESIGN, SETUP AND MEASUREMENTS ................. 22

3.1 Wave Flume and Wave Generation ............................................................................... 23

3.2 Description of the Wavemaker ....................................................................................... 26

3.3 Artificial Beach .............................................................................................................. 27

3.4 Measurement of Wave Height and Run-Up ................................................................... 28

3.5 Breakwater Model Set-Up .............................................................................................. 29

3.5.1 Rectangular foam and plastic model set-up.................................................... 31

3.5.2 PVC models:angle and semi-circular models ................................................ 32

CHAPTER 4 EXPERIMENTAL RESULTS ........................................................................ 34

5

4.1 Reference Case ............................................................................................................... 34

4.2 Plastic Rectangular Model ............................................................................................. 36

4.3 Rectangular Foam Model ............................................................................................... 40

4.4 PVC Saw-Tooth Shaped Angle Model .......................................................................... 44

4.5 PVC Semi-Circular Continuous Bump Model ............................................................... 46

CHAPTER 5 ANALYSIS AND DISCUSSION ................................................................... 48

5.1 Rectangular Model Comparison, Foam Vs Plastic ........................................................ 48

5.1-1 Run-up vs. wave amplitude on beach with 5 degree slope ............................ 48

5.1-2 Effect of model length on run-up reduction for 5 degree beach .................... 51

5.1-3 Run-up vs. wave amplitude on beach with 10 degree slope .......................... 54

5.1-4 Effect of model length on run-up reduction for 10 degree beach .................. 57

5.2 PVC Model Comparison: Angle vs Semi-Circular ........................................................ 60

5.3 PVC model vs. Rectangular Models .............................................................................. 65

5.4 Experimental Plastic Rectangular Model vs. Mohandie’s (2008) Numerical Results

Regarding Optimal Breakwater Length .................................................................................... 68

5.5 Rectangular Models 5 ft Breakwater Spacing Configuration ....................................... 71

5.6 Errors and Accuracies .................................................................................................... 77

CHAPTER 6 Conclusion ....................................................................................................... 78

6.1 Summary of work and findings ...................................................................................... 78

6.2 Recommendations .......................................................................................................... 80

REFERENCES .......................................................................................................................... 82

6

Table of Figures

Figure 2.1-1: Sketch of wave propagation over a submerged breakwater and run-up on a beach 16

Figure 2.4-1: Existing numerical results on the effect of breakwater length on run-up reduction

(Mohandie 2008). .......................................................................................................................... 21

Figure 3.1-1: Experimental Setup Sketch ..................................................................................... 23

Figure 3.1-2: Experimental setup in the lab, blue is the wave gauge, red is the wavemaker,

orange is the end of the beach slope with angle measurer, and green is the ruler to measure water

depth before each trial ................................................................................................................... 24

Figure 3.3-1: Photo of beach set-up .............................................................................................. 27

Figure 3.3-2: Photo of beach set-up at 10 degrees with angle measurement ................................ 27

Figure 3.4-1: Photo of wave gauge set-up in the lab ................................................................... 29

Figure 3.5.1-3.5.1-1: Comparison of foam and plastic rectangular models ................................. 31

Figure 3.5.1-2: Height comparison of the foam model and plastic model in the flume .............. 32

Figure 3.5.2-3.5.2-1: Full length of the PVC and angle models. The legnth of both models is

about equal. However, there are only 12 humps for the angle model vs. 16 for the semi-circular

PVC model. ................................................................................................................................... 33

Figure 3.5.2-3.5.2-2: Height comparison of the semi-circular PVC and angle models ................ 33

Figure 5.1-1-1: Run-up of a solitary wave on 5 degree beach after propagating over a plastic

rectangular breakwater model. ...................................................................................................... 49

Figure 5.1-1-2: Run-up of a solitary wave on 5 degree beach after propagating over a foam


Figure 5.1-1-3: Plastic vs. Foam Run-up at 5 degree, L=5 ft ....................................................... 50

7

Figure 5.1-1-4: Plastic vs. Foam Run-up at 5 degree, L =10 ft .................................................... 51

Figure 5.1-2-1: Plot of run-up reduction vs. the ratio of breakwater model length over

wavelength for α around 0.17; green triangles: plastic rectangular model, red squares: foam

rectangular model.......................................................................................................................... 52







Figure 5.1-3-1: Run-up of a solitary wave on 10 degree beach after propagating over a plastic


Figure 5.1-3-2: Run-up of a solitary wave on 10 degree beach after propagating over a foam


Figure 5.1-3-3: Plastic vs. Foam Run-up at 10 degree, 5 ft L ....................................................... 56

Figure 5.1-3-4: Plastic vs. Foam Run-up at 5 degree, 10 ft L....................................................... 56







8




Figure 5.1-4-4: Model length vs. run-up reduction for 10 degree beach – smaller amplitudes .... 59

Figure 5.2-1: Comparison of PVC models: Circular vs. Angle on 10 degree beach .................... 60

Figure 5.2-2: Comparison of PVC models: Circular vs. Angle on 10 degree beach .................... 61

Figure 5.2-3: PVC Model, Run-up Reduction Normalized by Model Height 5 degree ............... 63

Figure 5.2-4: PVC Model, Run-up Reduction Normalized by Model Height 10 degree ............. 63

Figure 5.3-1:Experimental Results from Mohandie (2007); Rectangular Rigid model 5 degree

slope; d/h of 0.65........................................................................................................................... 66

Figure 5.3-2: Experimental results PVC model run-up; 5 degree slope ....................................... 67

Figure 5.4-1: Numerical vs. Experimental Results Plastic Rectangular Models .......................... 68

Figure 5.4-2: Numerical vs. Experimental Results Foam Model ................................................. 69

Figure 5.5-1: Normal Experimental Setup with 5 ft model used for comparison......................... 71

Figure 5.5-2: Experimental Setup of breakwater model with spacing .......................................... 72

Figure 5.5-3: Plastic Model with spacing comparisons 5 degree ................................................. 75

Figure 5.5-4: Foam Model with spacing comparison 5 degree .................................................... 75

Figure 5.5-5: Plastic Model with spacing comparisons 10 degree ............................................... 76

Figure 5.5-6: Plastic Model with spacing comparisons 10 degree ............................................... 76

9

Table of Tables

Table 2.4-1: Effect of reef length L on reducing wave run-up R for d/h of 0.3 ........................... 20

Table 3.2-1: Sample Calibration Results for the Wavemaker ...................................................... 26

Table 4.1-1: Reference case, 5 degree beach slope ...................................................................... 35

Table 4.1-2: Reference case, 10 degree beach slope .................................................................... 35

Table 4.2-1: Plastic Rectangular Model, L = 2.5 ft, 5 degree slope ............................................. 36

Table 4.2-2: Plastic Rectangular Model, L = 5 ft, 5 degree slope ................................................ 36

Table 4.2-3: Plastic Rectangular Model, L = 7.5 ft, 5 degree slope ............................................. 37

Table 4.2-4: Plastic Rectangular Model, L = 10 ft, 5 degree slope .............................................. 37

Table 4.2-5: Plastic Rectangular Model, L = 2.5 ft, 10 degree slope ........................................... 38

Table 4.2-6: Plastic Rectangular Model, L = 5 ft, 10 degree slope .............................................. 38

Table 4.2-7: Plastic Rectangular Model, L = 7.5 ft, 10 degree slope ........................................... 39

Table 4.2-8: Plastic Rectangular Model, L = 10 ft, 10 degree slope ............................................ 39

Table 4.3-1: Rectangular Foam Model, L = 2.5 ft, 5 degree slope ............................................... 40

Table 4.3-2: Rectangular Foam Model, L = 5 ft, 5 degree slope .................................................. 40

Table 4.3-3: Rectangular Foam Model, L = 7.5 ft, 5 degree slope .............................................. 41

Table 4.3-4: Rectangular Foam Model, L = 10 ft, 5 degree slope ................................................ 41

Table 4.3-5: Rectangular Foam Model, L = 2.5 ft, 10 degree slope ............................................. 42

Table 4.3-6: Rectangular Foam Model, L = 5 ft, 10 degree slope ................................................ 42

Table 4.3-7: Rectangular Foam Model, L = 7.5 ft, 10 degree slope ............................................. 43

Table 4.3-8: Rectangular Foam Model, L = 10 ft, 10 degree slope .............................................. 43

Table 4.4-1: PVC Angle Model, L1, 5 degree slope ..................................................................... 44

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Table 4.4-2: PVC Angle Model, L2, 5 degree slope ..................................................................... 44

Table 4.4-3: PVC Angle Model, L1, 10 degree slope ................................................................... 45

Table 4.4-4: PVC Angle Model, L2, 10 degree slope ................................................................... 45

Table 4.5-1: PVC Circular Model, L3, 5 degree slope .................................................................. 46

Table 4.5-2: PVC Circular Model, L4, 5 degree slope .................................................................. 46

Table 4.5-3: PVC Circular Model, L3, 10 degree slope ................................................................ 47

Table 4.5-4: PVC Circular Model, L4, 10 degree slope ................................................................ 47

Table 5.2-1:Run-up Reduction for all four PVC model setup 5 degree ....................................... 62

Table 5.2-2: Run-up Reduction for all four PVC model setup 10 degree .................................... 62

Table 5.4-1: Optimal Model Length based on Rectangular Plastic Models ................................. 69

Table 5.4-2: Run-up Reduction for PVC Models ......................................................................... 70

Table 5.4-3 Run-up Reduction for PVC Models .......................................................................... 71

Table 5.5-1: Plastic Rectangle 5 ft with spacing (5 ft) 5 degree ................................................... 72

Table 5.5-2: Plastic Rectangle 5 ft with spacing (5 ft) 10 degree ................................................. 73

Table 5.5-3: Foam Rectangle 5 ft with spacing (5 ft) 5 degree .................................................... 73

Table 5.5-4: Foam Rectangle 5 ft with spacing (5 ft) 5 degree .................................................... 74

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CHAPTER 1 INTRODUCTION

1.1 Technical Background

A long tidal sea wave, commonly known as a tsunami, is caused by a massive

displacement of water often as a result of an earthquake, landslide or volcanic eruption. The

abrupt change in land mass creates a violent push on the ocean, creating tsunami waves that can

travel in deep ocean as fast as a commercial jet. As the wave approaches shallow water near the

coastline, the speed of the wave decreases, but the amplitude, or height of the wave increases.

The tsunami wave, lasting for hours, can cause major damage to coastal communities. In 2004,

the Indian Ocean tsunami and in 2011, the tsunami in Japan have both created a great deal of

damage wiping out almost everything in its vicinity. Locally in Hawaii, the 2011 tsunami was

of a smaller scale. The long travel time of the tsunami from Japan to Hawaii also allowed time

for evacuation in Hawaii if needed. However, the 2011 tsunami still incurred a significant

amount of damage in Hawaii. According to the state’s estimate, the tsunami damage totaled

$30.6 million (Hawaii 24/7). However, a later FEMA report estimated the damage total at $6.2

million (Insurance Journal), and a congressional research service report stated the damage at

“tens of millions of dollars” (Nanto 2011). The disaster preparedness and tsunami warning

systems are working and are saving lives, but more can be done. The aftermath of any tsunami is

often the rebuilding of lost homes, and shattered businesses. Rather than just a warning system,

the tsunami itself needs to be mitigated, if possible.

Areas prone to tsunami, such as Japan, have built breakwaters, which are natural or man-

made structures used to mitigate the tsunami wave by either stopping the wave or absorbing the

impact/energy of the wave. Commonly used breakwaters are above water, also known as

seawalls. In Japan, about 40% of the coast have seawalls – these are extremely important as

13

areas near the epicenter of the earthquake have little to no time to evacuate. In the 2011 tsunami

in Japan, the first tsunami wave hit the coast in less than 30 minutes after the earthquake. With

such little time to evacuate, it is important to have an effective tsunami mitigation in place.

Underwater breakwaters, in combination with other tsunami mitigation methods, could help

reduce the damage of the tsunami waves.

1.2 Literature Review

Many studies have been conducted on tsunamis, and on breakwaters and reefs as

potential mitigating measures against tsunamis. To list a few, Liu, Cho, Briggs, Synolakis and

Kanoglu (1995) carried out a joint numerical and experimental study on solitary wave run-up on

conical island. They found that the leeward side the island can actually experience a larger

tsunami wave height than the windward side due to long waves wrapping around the island.

Chang and Liou (2007) studied the transmission and reflection of tsunami on submerged

trapezoidal breakwater using the matching method based on the linear wave equations, i.e., first

separate the flow domain into different regions, and then solve for the analytical solution for

each region with matching conditions at the interface between two neighboring regions. In their

analytical study, they found that the top plane width (i.e., the top plane length along the wave

propagation direction) of the breakwater plays a major role in wave reflection. Mohandie (2008,

2012) investigated the effects of vegetation and submerged reef/breakwater in reducing long-

wave run-up by using both numerical stimulations and experimental study. He found through

numerical simulation that when the length of a submerged rectangular breakwater or reef is twice

the wavelength, it has the maximum reduction rate on run-up. However, this particular numerical

result was not studied or verified in the wave tank experiments in Mohandie’s research (2008,

2012). Shimabuku (2012) examined the effect of lagoon spacing on run-up reduction and

14

submerged breakwater. Each study’s focus was different, but all studies showed that submerged

breakwaters and reefs are effective in run-up reduction to a certain degree. In both Mohandie

and Shimabuku’s study, the shape of the breakwater was rectangular. The effect of the geometry

and material properties of the breakwater were not investigated.

1.3 Objective of Present Study

The objectives of the present study are:

1) to better understand the interaction between long waves and submerged structures with

different geometry and material properties;

2) to verify the numerical result that an optimal breakwater length exists and that the

optimal length of the breakwater is two times the wavelength by comparing with the

experimental data gathered in this study;

3) to seek optimal configuration and material of submerged breakwaters that can help to

reduce long wave run-up more effectively.

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CHAPTER 2 THEORY, GOVERNING EQUATIONS AND EXISTING

NUMERICAL RESULTS

In this chapter, the theory and equations that can be used to mathematically model the

long wave propagation and run-up are described briefly. More detailed description can be found

in Mohandie (2008) and Shimabuku (2012).

2.1 Governing Equations for Long Wave Propagation

Figure 2.1-1 shows a sketch of the physical set-up for the problem of interest for this

thesis study. ho is the still water depth, a is the amplitude of the generated wave, ζ is the wave

height, h is the water depth, L is the length of the submerged breakwater, d is the height of the

submerged breakwater, β is the beach slope, and R is the run-up.

The Boussinesq wave model provides a good approximation of non-linear and dispersive

long waves. Since our present experimental study is for waves travelling in a narrow rectangular

channel, a one-dimensional Boussinesq equation can be used to model the waves. The continuity

equation and momentum equation for long wave propagation on smooth bed based on the

Boussinesq model are as follows:

a

ho h

h

ζ

R

L

d breakwater β

x

Figure 2.1-1: Sketch of wave propagation over a submerged breakwater and run-up on a beach

16

( )[ ] 0=++ xt uh ζζ (2.1)

031 2 =−++ xxtxxt uhuuu ζ (2.2)

where ζ is the water surface elevation, u the depth-averaged velocity in the x-direction, h the still

water depth, and t time, suffices represent partial derivatives with respect to that variable.

The variables in equations (2.1) and (2.2) are non-dimensionalized with the constant still

water depth 0h as follows:

,*

0hζζ = ,*

0hxx =

ght

chtt

00

0

**== ,

0

*cuu = (2.3)

where g is gravitational acceleration, 00 ghc = is the linear long wave speed, and * represents

dimensional variables.

2.2 Governing Equation for Long Wave Run Up

During wave run-up, the water depth decreases rapidly, therefore the non-linear effect is

prominent, and the dispersive effect can be ignored. The classical nonlinear and non-dispersive

shallow water equations can be used to model long wave run-up. These equations are:

0=∂∂

+∂∂

xQ

tζ

(2.4)

17

02

=∂∂

+

∂∂

+∂∂

xH

HQ

xtQ ζ (2.5)

where H = h + ζ and Q = uH.

Equation (2.4) and equation (2.5) are equivalent to equation (2.1) and equation (2.2)

without the dispersive factor.

2.3 A Solitary Wave as the Initial Wave

A solitary wave is a single displacement of water above the sea-level and is often used to

model a long wave such as a tsunami in academic research. A mathematical description of the

solitary wave is given by Eqn 2.6 based on the Boussinesq solution (Teng and Wu 1992, Teng

1997):

( ) ( )[ ]( )[ ]ctxxk

ctxxkhtxo

o

−−+−−

= 2

2

tanh1sec,α

αζ (2.6)

where ( )αα

68.0143

+=k , wave speed

( )( ) ( ) ( )[ ]ααα

ααα

−+++

+= 1ln1

2316

2

2

c , and normalized

wave amplitude ha

=α . The wave amplitude can also be related to the effective wavelength as

follows:

( )( )

+−

++=

21

21

1

01.0199.01

01.0199.01

ln1

α

αλke (2.7)

18

( )( )

+−

++=

21

21

5

05.0195.01

05.0195.01

ln1

α

αλke (2.8)

where λe1 and λe5 represent the wavelength between the locations where the water surface

elevation is equal to 1% and 5% of the wave amplitude, respectively. This can also be expressed

as For this study, λe1 was used.

2.4 Existing Numerical Results

The above long wave equations were solved numerically in two previous studies from

our research group (Mohandie 2008 and Shimabuku 2012) to simulate long wave propagation

over submerged reef and breakwaters as shown in Figure 2.1-1. One of the interesting results

from Mohandie (2008)’s numerical simulation was that the length of the submerged breakwater

was found to play a role in reducing the final long wave run-up on a beach. First, it was observed

that if the submerged object is too short, it will not have a significant effect on reducing the run-

up of a long wave. On the other hand, it was also discovered that the reduction effect does not

increase with the length infinitely. Instead, the numerical results showed that there was an

optimal length that would lead to the maximum run-up reduction possible. The specific results

for a sample case with reef height d/ho = 0.3 (normalized breakwater height) and the beach angle

β = 5o were summarized in a later paper (Mohandie and Teng 2012) and also presented in Table

2.4-1 and Figure 2.4-1 here:

19

Table 2.4-1: Effect of reef length L on reducing wave run-up R for d/h of 0.3

initial amplitude α wavelength λ reef length L/λ run-up reduction % 0.1 22.2 0.5 21 0.75 22 1 28 2 32 3 28 0.2 16.0 0.5 15 0.75 20 1 20 2 25 3 24

20

Numerical Results

0

5

10

15

20

25

30

35

0 0.5 1 1.5 2 2.5 3 3.5

model length/wavelength

% re

duct

ion

in ru

n-up

α = 0.1

α = 0.2

Figure 2.4-1: Existing numerical results on the effect of breakwater length on run-up reduction for d/h of 0.30 (Mohandie 2008).

These results indicated that short reefs are less effective than the long reefs in reducing

the wave run-up. However, as the reef length increases beyond twice the wavelength, the

reduction rate starts to drop again. The results showed that when the reef length is approximately

twice the wavelength, the run-up reduction is maximized. The averaged observed reduction rate

due to wave propagating over the submerged breakwaters is roughly 24%. Note that this is for a

case with breakwater height d/ho = 0.3, namely, the breakwater height is 30% of the water depth.

Based on past work, if the breakwater height d is increased, then the reduction rate for run-up

would be higher.

The above numerical results have not been validated by experiments. In addition, in the

numerical studies, only rectangular submerged breakwater models were considered. The reason

is that the numerical models can only simulate submerged bodies with relatively simple

21

geometries and smooth surfaces. Other shapes were not considered since significantly irregular

shapes with abrupt variations can cause the numerical schemes to become unstable. In actual

engineering applications, beyond simple geometries, we are also interested in examining whether

submerged breakwaters with complex geometries, such as those with saw-tooth shaped surface

shapes, would be more effective in reducing wave run-up. Also, besides smooth and rigid surface

materials, we are interested in investigating whether sponge-type of surface material may lead to

more reduction in run-up. These complex cases are difficult to model theoretically or

numerically, and require wave tank experiments to study them.

The objectives of the present study are to carry out wave tank experiments to validate the

numerical results obtained and presented in Mohandie (2008) and Mohandie and Teng (2012),

and to examine submerged breakwater models of complex geometry and different surface

materials in order to seek the most effective design for reducing long wave run-up on a beach.

CHAPTER 3 EXPERIMENTAL DESIGN, SETUP AND MEASUREMENTS

As stated in the earlier sections, the main focus of the present study is to perform wave

tank experiments in order to further investigate the phenomenon of long waves propagating over

submerged breakwater or reefs and examine how the submerged structures would reduce the

wave run-up on dryland. While theoretical modeling and numerical simulations have the

advantage of studying a large number of cases without much material cost such as constructing

physical models and purchasing supplies, they do have limitations. For example, most of the

wave theories are based on certain assumptions, and numerical schemes all have accuracy and

instability issues. They can study cases with simple geometries but may encounter difficulties

modeling complex structures. Because of these, lab experiments remain as a very valuable tool to

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investigate various fluid and wave phenomena. The dominant methodology used in this study is

lab experiments. In this chapter, the detailed experimental set-up, model construction, and

measurement instruments are described.

3.1 Wave Flume and Wave Generation

The experiments were conducted in a transparent wave flume with dimensions of 6 in

width, 1.25 ft depth, and 35 ft length. Wave generation is done by a wavemaker at one end of

the flume. Figure 3.1-1 illustrates a solitary wave of amplitude α being created in still water of

depth ho with a breakwater model of height d and length L. The angle β is the angle of the

artificial beach, and R is the wave run-up. Symbols WG2 and WG1 represent the wave gauges.

Figure 3.1-2 shows a photo of the experimental setup in the lab.

In this study, the angle of the beach was set at 5 degrees and 10 degrees. Four different

breakwater models each with varying lengths were tested (refer to model setup). The wave

gauges were set upstream and downstream of the breakwater model. A computer program was

used to generate a single solitary wave from the wave maker. Figure 3.1-3 shows the wavemaker

R

L

d breakwater model β

x

WG1 WG2

a

h0

wavemaker

Figure 3.1-1: Experimental Setup Sketch

23

setup. The amplitudes entered into the program starts from 0.05h0 to 0.275 h0 with increments of

0.025 h0. Wave gauge 1 was intended to measure the actual amplitude created by the wavemaker

upstream of the breakwater model.

Figure 3.1-2: Experimental setup in the lab, blue is the wave gauge, red is the wavemaker, orange is the end of the beach slope with angle measurer, and green is the ruler to measure

water depth before each trial

24

Figure 3.1-3: Photo of the wavemaker setup

Figure 3.1-4: Photo of the flume with wavemaker generating periodic waves

25

3.2 Description of the Wavemaker

The wavemaker used in this study was designed and built by a former ORE Ph.D. student

Richard Carter. The wavemaker is a computer controlled piston-type wavemaker. It can generate

periodic waves (Figure 3.1-4), solitary waves or any other waves that the user would like by

inputting the correct wave data in the computer.

While the wavemaker is an excellent tool in performing wave tank experiments, the

generated wave amplitude and period should be measured by a wave gage because in some cases,

the generated wave height and period do not match the input data completely. As an example, the

following calibration results in Table 3.2-1 give us an idea about the accuracy of the wavemaker

for periodic waves:

Table 3.2-1: Sample Calibration Results for the Wavemaker

Input

wave amplitude (in)

Generated

wave amplitude (in)

Input

wave period (sec)

Generated

wave period (sec)

Case 1 0.5 0.35 0.5 0.45

Case 2 1 0.92 1 1

For solitary waves, the wavemaker has a similar level of accuracy for the wave amplitude

and wave form.

26

3.3 Artificial Beach

The beach model was constructed by a plane plexi-glass board braced with uni-struts and

rested near one end of the flume. The setup was made such that the angle of the beach β is

adjustable. Figures 3.3.-1 and 3.3-2 show the beach set-up in the experiments.

Figure 3.3-1: Photo of beach set-up

Figure 3.3-2: Photo of beach set-up at 10 degrees with angle measurement

27

3.4 Measurement of Wave Height and Run-Up

To measure the wave height in this study, two capacitance – type wave gauges were used,

one upstream of the breakwater and one downstream of the breakwater. The first gauge

measured the initial wave amplitude, and the second gauge measured the effects of the

breakwater on the wave over time. The wave gauges were made by a Japanese company JFE

Advantech Co. (Model ACH-600RS). There are a total of three gages available in our hydraulics

lab. We have performed tests to examine the accuracy of the three commercialized gauges.

Specifically, we used the gauges to measure the static water depth in a wave tank at different

depth levels. Then we compared the gauge readings with the depth measured by a ruler. The

results from the two measurement techniques matched with each other closely. The relative

difference was 1.5%, 4.7%, 1.3% for wave gage #1, 2 and 3, respectively.

Wave inundation (D) on the beach shown in Figure 3.1-1 was measured manually by

marking the highest point that the wave reaches on the artificial beach. Then a measuring tape

was used to measure the distance from the still waterline to the marked point. Run-up R was

then calculated using the following relationship R = D sin β. Figure 3.4-1 shows the wave gauge

setup.

28

Figure 3.4-1: Photo of wave gauge set-up in the lab

3.5 Breakwater Model Set-Up

In this study, the main focus is to determine the optimal configuration of a submerged

breakwater for effective run-up reduction. The three factors that were examined are the

breakwater length and the breakwater geometry and material properties. In the two previous

studies conducted by Ravi Mohandie (2008) and Nathan Shimabuku (2012), different conditions

were tested and different results were obtained regarding the optimal breakwater length.

Mohandie found through numerical simulations that the optimal breakwater length was twice the

wavelength. However, Shimabuku’s experimental conditions did not include a breakwater

model as long as twice the wavelength and therefore Mohandie’s findings have not been tested

and verified by experiments. Moreover, in both of those studies only a rectangular breakwater

29

model was used. For this study, four new cases were investigated in order to achieve the

following:

1) test and verify the proposed optimal breakwater length being twice the wavelength

by performing wave flume experiments;

2) test and observe the effects that different geometry and material property of

breakwater has on run-up reduction;

3) based on the experimental results from this study, make recommendations for

optimal breakwater geometry that can be more effective in reducing wave run-up on

coastal land.

30

3.5.1 Rectangular foam and plastic model set-up

Multiple plastic rectangular breakwater models were tested in this study. Their length

was 2.5 ft, 5 ft, 7.5 ft and 10 ft. The height d of the models was 1 inch. The width of the model

encompasses the entire flume width at 6 inches. The water depth h in the experiments was 3

5/16 in, resulting in a relative breakwater height of d/h = 0.30, which matches with the value for

this parameter in Mohandie’s (2008) numerical study. The wave amplitude in the present study

was varied in different testing cases. We note from eqn (2.7) that the wavelength of a solitary

wave is related to the wave amplitude. Specifically, the higher the wave amplitude, the shorter

the wavelength. The four different model lengths paired with ten different wave amplitudes

provided a set of experimental data where the length of the model is less than one wavelength of

the wave, between one and two times the wavelength, and greater than two times the wave

length. In addition, porous foam models with the same geometry of the plastic rectangular

models were tested. To keep the foam models from floating, a thin aluminum plate was glued to

the bottom of the foam models.

Figure 3.5.1-1: Photo comparison of foam (top and bottom) and plastic (middle) rectangular models

31

Figure 3.5.1-2: Photo of height comparison of the foam model and plastic model in the

flume, the foam model is on the left and the plastic model is on the right

3.5.2 PVC models:angle and semi-circular models

In addition to the rectangular models, two “speed bump” variant models with PVC semi-

circles and angles were constructed. Figure 3.5.2-1 shows the full length of the model. The two

models are made to be similar to each other, but due to material constraints, there are slight

differences. The height of the semi-circular model is 1.22 in or 3.2 cm whereas the height of the

angle is 1.77 in or 4.5 cm as shown in Figure 3.5.2-2. The periodic semi-circular PVC model has

16 humps whereas the angle model has 12 humps. Two lengths of the model were tested (i.e., at

full length and half length). The full length of the PVC semi-circular model is about 37 in or 94

cm, whereas the full length of the angle model is 39.4 in or 100 cm. The water depth was 3 5/16

in or 8.4 cm.

32

Figure 3.5.2-1: Full length of the PVC and angle models. The legnth of both models is about equal. However, there are only 12 humps for the angle model vs. 16 for the semi-

circular PVC model.

Figure 3.5.2-2: Height comparison of the semi-circular PVC and angle models

33

CHAPTER 4 EXPERIMENTAL RESULTS

In this study, a large number of wave tank experiments were carried out to investigate the

effect of different types of submerged breakwater models on long wave run-up reduction. In

order to establish a base case or reference case for comparison purposes, the first test we run was

wave propagating over a flat tank bottom with no breakwater models and then running up over

the beach. After this case was completed, we run experiments on waves propagating over various

submerged breakwater models including the plastic rectangular models, the foam rectangular

models, saw-tooth shaped angle models and the periodic semi-circular bump models. In this

chapter, we present the results from all the experimental cases, displaying them in tables in the

following sections. The results are for wave inundation and run-up against different initial wave

amplitude measured by the wave gauge WG1. Each case was ran once. All the results have been

non-dimensionalized by the still water depth which was 3 5/16 in in all the cases in this study.

4.1 Reference Case

The results of the reference case are shown in Table 4.1-1 and 4.1-2. These are the

results of run-up with no submerged breakwater model in the flume. The measurements are

divided by the water depth of 3 and 5/16 inches (or 8.4 cm).

34

Table 4.1-1: Reference case, 5 degree beach slope

5 degree reference

Amplitude Inundation Run-Up

0.032 0.524 0.046

0.063 1.155 0.101

0.075 1.583 0.138

0.117 1.810 0.158

0.127 2.179 0.190

0.148 2.869 0.250

0.174 3.667 0.320

0.207 4.167 0.363

0.233 4.643 0.405

0.258 5.286 0.461

Table 4.1-2: Reference case, 10 degree beach slope

10 degree reference


0.018 0.357 0.062

0.049 0.690 0.120

0.079 1.048 0.182

0.107 1.655 0.287

0.112 1.714 0.298

0.139 2.321 0.403

0.169 2.667 0.463

0.198 3.071 0.533

0.244 3.655 0.635

0.258 3.750 0.651

35

4.2 Plastic Rectangular Model

The results of the plastic rectangular model with 5 degree beach slope at model lengths

2.5 ft, 5 ft, 7.5 ft, and 10 ft are shown below.

Table 4.2-1: Plastic Rectangular Model, L = 2.5 ft, 5 degree slope

Plastic Rectangle 2.5 ft 5 degrees Amplitude Inundation Run-Up

0.018 0.417 0.036 0.055 0.833 0.073 0.088 1.321 0.115 0.105 1.786 0.156 0.124 2.202 0.192 0.137 2.786 0.243 0.175 3.500 0.305 0.207 4.226 0.368 0.218 4.583 0.399 0.250 5.179 0.451

Table 4.2-2: Plastic Rectangular Model, L = 5 ft, 5 degree slope

Plastic Rectangle 5 ft 5 degree Amplitude Inundation Run-Up

0.019 0.298 0.026 0.057 0.690 0.060 0.077 1.405 0.122 0.107 1.714 0.149 0.121 2.024 0.176 0.132 2.440 0.213 0.162 3.036 0.265 0.188 3.571 0.311 0.210 3.929 0.342 0.245 4.643 0.405

36


Plastic Rectangle 7.5 ft 5 degree


0.020 0.333 0.029

0.063 0.905 0.079

0.071 1.333 0.116

0.110 1.714 0.149

0.123 2.190 0.191

0.139 2.702 0.236

0.164 3.071 0.268

0.208 3.976 0.347

0.229 4.393 0.383

0.257 4.726 0.412


Plastic Rectangle 10 ft 5 degree


0.040 0.357 0.031

0.048 0.631 0.055

0.083 1.286 0.112

0.119 1.845 0.161

0.126 2.036 0.177

0.143 2.917 0.254

0.175 3.369 0.294

0.200 3.655 0.319

0.230 4.690 0.409

0.257 4.857 0.423

37

The results of the plastic rectangular model with 10 degree beach slope at model lengths



Plastic Rectangle 2.5 ft 10 degrees


0.021 0.286 0.050

0.061 0.976 0.170

0.073 1.238 0.215

0.108 1.286 0.223

0.140 1.595 0.277

0.175 2.060 0.358

0.182 3.060 0.531

0.190 3.238 0.562

0.219 3.536 0.614

0.271 3.893 0.676




0.018 0.405 0.070

0.048 0.869 0.151

0.071 1.012 0.176

0.106 1.417 0.246

0.123 1.786 0.310

0.146 2.024 0.351

0.165 2.500 0.434

0.194 3.310 0.575

0.224 3.548 0.616

0.257 3.750 0.651

38


Plastic Rectangle 7.5 ft 10 degree


0.019 0.381 0.066

0.052 0.726 0.126

0.104 1.107 0.192

0.119 1.429 0.248

0.152 1.750 0.304

0.157 2.083 0.362

0.171 2.536 0.440

0.202 2.988 0.519

0.223 3.298 0.573

0.250 3.571 0.620




0.019 0.667 0.116

0.062 1.238 0.215

0.069 1.357 0.236

0.090 1.429 0.248

0.125 1.643 0.285

0.162 2.083 0.362

0.185 2.500 0.434

0.187 2.560 0.444

0.226 2.988 0.519

0.268 3.405 0.591

39

4.3 Rectangular Foam Model

The results of the rectangular foam model with 5 degree beach slope at model lengths 2.5

ft, 5 ft, 7.5 ft, and 10 ft are shown below.

Table 4.3-1: Rectangular Foam Model, L = 2.5 ft, 5 degree slope

Foam Rectangle 2.5 ft 5 degrees Amplitude Inundation Run-Up

0.052 0.464 0.040 0.088 0.845 0.074 0.130 1.369 0.119 0.151 1.750 0.153 0.176 2.190 0.191 0.202 2.536 0.221 0.229 3.012 0.263 0.244 3.440 0.300 0.248 3.988 0.348 0.264 4.631 0.404

Table 4.3-2: Rectangular Foam Model, L = 5 ft, 5 degree slope

Foam Rectangle 5 ft 5 degree Amplitude Inundation Run-Up

0.052 0.393 0.034 0.085 0.940 0.082 0.118 1.167 0.102 0.152 1.679 0.146 0.181 2.226 0.194 0.212 2.560 0.223 0.236 2.976 0.259 0.245 3.476 0.303 0.249 3.905 0.340 0.282 4.464 0.389

40


Foam Rectangle 7.5 ft 5 degree


0.061 0.417 0.036

0.089 0.917 0.080

0.124 1.524 0.133

0.152 1.917 0.167

0.170 2.190 0.191

0.198 2.405 0.210

0.217 3.071 0.268

0.230 3.274 0.285

0.242 3.750 0.327

0.277 4.631 0.404


Foam Rectangle 10 ft 5 degree


0.057 0.583 0.051

0.081 0.964 0.084

0.106 1.357 0.118

0.131 1.810 0.158

0.163 2.071 0.181

0.199 2.679 0.233

0.219 3.095 0.270

0.230 3.286 0.286

0.251 3.786 0.330

0.271 4.048 0.353

41

The results of the rectangular foam model with 10 degree beach slope at model lengths



Foam Rectangle 2.5 ft 10 degrees Amplitude Inundation Run-Up

0.019 0.179 0.031 0.074 0.476 0.083 0.102 0.798 0.139 0.119 1.107 0.192 0.167 1.512 0.263 0.196 1.940 0.337 0.206 2.214 0.385 0.226 2.536 0.440 0.255 2.750 0.478 0.281 3.119 0.542


Foam Rectangle 5 ft 10 degree Amplitude Inundation Run-Up

0.020 0.286 0.050 0.081 0.548 0.095 0.130 0.917 0.159 0.144 1.107 0.192 0.155 1.429 0.248 0.192 1.833 0.318 0.205 2.202 0.382 0.223 2.440 0.424 0.257 2.821 0.490 0.275 3.071 0.533

42


Foam Rectangle 7.5 ft 10 degree


0.044 0.274 0.048

0.092 0.595 0.103

0.117 0.881 0.153

0.137 1.107 0.192

0.174 1.536 0.267

0.167 1.702 0.296

0.195 2.024 0.351

0.218 2.202 0.382

0.255 2.667 0.463

0.274 2.798 0.486


Foam Rectangle 10 ft 10 degree


0.045 0.310 0.054

0.092 0.571 0.099

0.108 0.786 0.136

0.132 1.048 0.182

0.167 1.321 0.229

0.200 1.810 0.314

0.213 2.083 0.362

0.213 2.238 0.389

0.248 2.607 0.453

0.263 2.643 0.459

43

4.4 PVC Saw-Tooth Shaped Angle Model

The results of the PVC angle model with 5 degree beach slope at model lengths L1 =

19.7 in and L2 = 39.4 in are shown below.

Table 4.4-1: PVC Angle Model, L1, 5 degree slope

Angle L1 5 degree Amplitude Inundation Run-Up

0.019 0.464 0.040 0.049 0.786 0.068 0.071 1.083 0.094 0.119 1.524 0.133 0.125 1.821 0.159 0.160 2.107 0.184 0.183 2.548 0.222 0.210 2.964 0.258 0.243 3.500 0.305 0.274 3.679 0.321



0.019 0.214 0.019 0.064 0.583 0.051 0.101 0.810 0.071 0.121 1.107 0.096 0.131 1.452 0.127 0.155 1.714 0.149 0.188 2.036 0.177 0.211 2.333 0.203 0.238 2.607 0.227

44

The results of the PVC Angle model with 10 degree beach slope at model lengths L1 =

19.7 in and L2 = 39.4 in are shown below.



0.020 0.286 0.050 0.083 0.512 0.089 0.113 0.714 0.124 0.130 1.024 0.178 0.149 1.262 0.219 0.179 1.690 0.294 0.186 1.881 0.327 0.208 2.167 0.376 0.243 2.464 0.428 0.263 2.750 0.478



0.020 0.155 0.027 0.080 0.357 0.062 0.113 0.571 0.099 0.133 0.798 0.139 0.136 1.024 0.178 0.177 1.238 0.215 0.180 1.500 0.260 0.208 2.000 0.347 0.245 1.917 0.333 0.274 2.214 0.385

45

4.5 PVC Semi-Circular Continuous Bump Model

The results of the PVC semi-circular bump model with 5 degree beach slope at lengths

L3= 18.5 in and L4= 37 in are shown below.

Table 4.5-1: PVC Circular Model, L3, 5 degree slope

Circular L3 5 degree Amplitude Inundation Run-Up

0.020 0.369 0.032 0.086 0.726 0.063 0.106 1.071 0.093 0.133 1.607 0.140 0.155 1.905 0.166 0.175 2.310 0.201 0.190 2.857 0.249 0.208 3.179 0.277 0.240 3.750 0.327 0.268 4.548 0.396



0.020 0.262 0.023 0.077 0.726 0.063 0.085 1.095 0.095 0.131 1.429 0.125 0.126 1.881 0.164 0.155 2.321 0.202 0.180 2.667 0.232 0.205 3.226 0.281 0.239 3.536 0.308 0.271 4.083 0.356

46

The results of the PVC Circular model with 10 degree beach slope at lengths L3= 18.5 in

and L4= 37 in are shown below.



0.019 0.333 0.058 0.060 0.643 0.112 0.100 1.071 0.186 0.113 1.333 0.232 0.121 1.464 0.254 0.148 1.845 0.320 0.182 2.321 0.403 0.207 2.560 0.444 0.233 2.917 0.506 0.271 3.310 0.575



0.021 0.250 0.043 0.069 0.595 0.103 0.110 0.976 0.170 0.123 1.262 0.219 0.157 1.619 0.281 0.144 1.798 0.312 0.173 2.083 0.362 0.205 2.524 0.438 0.235 2.857 0.496 0.257 3.036 0.527

47

CHAPTER 5 ANALYSIS AND DISCUSSION

In this chapter, the experimental data are analyzed and discussed. We are especially

interested in comparing the effect of different types of submerged breakwater models in reducing

long wave run-up. The experimental data are also compared with Mohandie’s (2008) numerical

results regarding the optimal breakwater length in run-up reduction.

5.1 Rectangular Model Comparison, Foam Vs Plastic

The experiment was conducted twice – once with beach slope of 5 degree and again with

a beach slope of 10 degree. The analysis of the 5 degree beach slope will be reviewed first,

followed by the 10 degree beach slope analysis.

5.1-1 Run-up vs. wave amplitude on beach with 5 degree slope

The graph in Figure 5.1-1-1 compares the run-up in the case of the plastic rectangular

models of length of 2.5, 5, 7.5, and 10 ft., with that in the reference case. Figure 5.1-1-2

compares the run-up results in the case of the foam rectangular models of length of 2.5, 5, 7.5,

and 10 ft., with that in the reference case.

48

Figure 5.1-1-1: Run-up of a solitary wave on 5 degree beach after propagating over a plastic rectangular breakwater model.

Figure 5.1-1-2: Run-up of a solitary wave on 5 degree beach after propagating over a foam rectangular breakwater model.

49

A linear best fit trend line was created. Except for the case with L=2.5 ft for the plastic

model, the run-up for all other models are marginally reduced as compared to the reference case.

The foam model shows a significant effect in decreasing run-up compared with the plastic model.

Moreover, increasing the length of the breakwater only offers slight improvements for both

models – economically, it would make more sense to build the shorter model. Figure 5.1-1-3

shows the comparison of the run-up results between the cases of the plastic vs. foam model of 5

ft. length. Figure 5.1-1-4 shows the comparison of the plastic vs. foam model of 10 ft. length.

Figure 5.1-1-3: Plastic vs. Foam Run-up at 5 degree, L=5 ft

50

Figure 5.1-1-4: Plastic vs. Foam Run-up at 5 degree, L =10 ft

In both cases, the plastic breakwater model results in only minor run-up reduction

whereas the foam model results in more significant reduction.

5.1-2 Effect of model length on run-up reduction for 5 degree beach

The three graphs below show the comparison of the plastic vs. the foam model at specific

amplitudes for the effect of model length on run-up reduction. For the below comparisons, note

that the amplitude for each model is slightly different, since the wave maker cannot create the

exact same wave each time. However, the difference in amplitude is small and should not affect

the results significantly. To compare run-up reduction, a linear best fit line was created for the

reference case. The run-up in the cases with the breakwater models is then compared to the best

fit line at the same amplitude in the reference case to find the run-up reduction percent. The best

51

fit line for the reference case is R = 1.8368α - 0.0205 (r2 = 0.9835), where R is the run-up and α

is the amplitude of the initial wave.

Figure 5.1-2-1: Plot of run-up reduction vs. the ratio of breakwater model length over wavelength for α around 0.17; green triangles: plastic rectangular model, red squares:

foam rectangular model

52





53

For all four comparisons, the foam model consistently resulted in better run-up reduction

than the plastic model. The run-up between the foam models of different lengths is similar in all

four amplitude ranges whereas the plastic model varies. The plastic model also seems to have

the same trend across the different amplitudes. In the plastic models, the best model lengths are

in-between one to two times the wavelength. The result thus far has shown that the longer

breakwater model does not necessarily perform the best. The optimal breakwater length will be

further discussed in Section 5.4.

5.1-3 Run-up vs. wave amplitude on beach with 10 degree slope

The graph in Figure 5.1-3-1 below compares the run-up in the case of the plastic

rectangular model of length of 2.5, 5, 7.5, and 10 ft, with that in the reference case. Figure 5.1-3-

2 compares the run-up results in the case of the foam rectangular models of length of 2.5, 5, 7.5,

and 10 ft., with that in the reference case.

Figure 5.1-3-1: Run-up of a solitary wave on 10 degree beach after propagating over a plastic rectangular breakwater model.

54

Figure 5.1-3-2: Run-up of a solitary wave on 10 degree beach after propagating over a foam rectangular breakwater model.

For the 10-degree beach slope, the plastic models seem to perform worst. However, just

as the case with the 5 degree beach slope, the foam model consistently performs better than the

plastic model. Figure 5.1-3-3 shows the comparison of the plastic vs. foam model of 5 ft. length.

Figure 5.1-3-4 shows the comparison of the plastic vs. foam model of 10 ft. length.

55

Figure 5.1-3-3: Plastic vs. Foam Run-up at 10 degree, 5 ft L

Figure 5.1-3-4: Plastic vs. Foam Run-up at 5 degree, 10 ft L

56

For the 10 degree beach slope, the plastic model did not show any improvement. The

foam model still consistently performs better.

5.1-4 Effect of model length on run-up reduction for 10 degree beach

The three graphs below show the comparison of the plastic vs. the foam model at specific

amplitudes for the effect of model length on run-up reduction. Eqn. 2.7 was used to find the

wavelength of the generated wave. The model length was then normalized by water depth, ho of

3 5/16 inches and then divided by the calculated wave length. To compare run-up reduction, a

linear best fit line was created for the reference case. The run-up in the cases with the

breakwater models is then compared to the best fit line at the same amplitude in the reference

case to find the run-up reduction percent. The best fit line for the reference case is R = 2.5858α

+ 0.0085 (r2 = 0.991), where R is the run-up and α is the amplitude of the wave.



57





58

For all three comparisons, the foam model consistently resulted in better run-up reduction

than the plastic model. It is clear that for the 10 degree beach test, the plastic models no longer

show a consistent trend.

Additional experiments were performed for waves of smaller amplitude over the plastic

rectangular models over the 10 degree beach by Mohandie. These results are shown in Figure

5.1.-4-4.

These results follow a similar trend to the results in the case with the 5 degree beach

slope, namely, there exists an optimal breakwater length with which the run-up reduction is the

maximum. However, it should be noted that for α = 0.062, the run-up reduction is unusually

high for a plastic rectangular model.

Figure 5.1-4-4: Model length vs. run-up reduction for 10 degree beach – smaller amplitudes

59

5.2 PVC Model Comparison: Angle vs Semi-Circular

The experiment was conducted twice – once with beach slope of 5 degree and again with

a beach slope of 10 degree. The water depth in the experiments was h = 3 5/16 in. The height of

the angle model was d = 1.77 in or d/h = 0.53. For the semi-circular model, the model height d =

1.26 in, or d/h = 0.38. Two model lengths were tested in each case: L1 = 18.5 in and L2 = 37 in

for the semi-circular model, and L3 = 19.7 in and L4 = 39.4 in for the angle model. The

experimental results of run-up vs. initial wave amplitude are shown below.

Figure 5.2-1: Comparison of PVC models: Circular vs. Angle on 10 degree beach

60

The Angle model performed better in both cases. More specifically, the semi-circular

model with length 18.5 inches performed the worst. The same model with twice the length

performed slightly better. The Angle model performed better than both semi-circular models –

with the longer Angle model doing even better. This increase in run-up reduction cannot be

solely attributed to the geometry, since the Angle models are higher. The detailed run-up

reduction is shown in the Table 5.2-1 and Table 5.2-2:

Figure 5.2-2: Comparison of PVC models: Circular vs. Angle on 10 degree beach

61

Table 5.2-1:Run-up Reduction for all four PVC model setup 5 degree

Run-up Reduction Summary 5 degree Amplitude

Range Circular Angle

L1 L2 L3 L4

0.019 - 0.020 0.0% 0.0% 0.0% 0.0% 0.049 - 0.086 53.8% 48.0% 1.0% 47.9% 0.071 - 0.106 46.4% 29.2% 14.7% 57.3% 0.119 - 0.133 37.6% 43.4% 33.0% 52.4% 0.125 - 0.155 37.1% 22.4% 24.1% 42.5% 0.155 - 0.175 33.1% 23.3% 32.6% 43.4% 0.180 - 0.190 24.4% 25.0% 29.8% 45.4% 0.205 - 0.211 23.5% 20.9% 29.1% 44.5% 0.238 - 0.243 22.4% 26.5% 28.3% 45.5% 0.268 - 0.274 15.9% 25.6% 33.5% 46.0%

Table 5.2-2: Run-up Reduction for all four PVC model setup 10 degree

Run-up Reduction Summary 10 degree Amplitude

Range Circular Angle

L1 L2 L3 L4

0.019 - 0.021 0.0% 32.1% 18.4% 55.8% 0.060 - 0.083 31.3% 44.7% 60.3% 71.1% 0.100 - 0.113 30.3% 41.9% 58.8% 67.0% 0.113 - 0.133 23.1% 32.7% 48.3% 60.8% 0.121 - 0.157 21.2% 32.2% 44.3% 50.5% 0.148 - 0.179 17.9% 18.1% 37.6% 54.0% 0.173 - 0.186 15.9% 20.5% 33.2% 45.0% 0.205 - 0.208 18.3% 18.5% 31.2% 36.5% 0.235 - 0.245 17.2% 19.3% 32.8% 48.2% 0.257 - 0.274 19.1% 21.7% 30.7% 46.3%

Based on past results, it is expected that the longer the model the better (in this case)

since the longest model (L2 and L4 about 40 in) for both the semi-circular and Angle model are

less than one wavelength. Moreover, it is important to note that the dimensions of the Circular

model and the Angle model are different. The Angle model is taller and slightly longer. Since

the model lengths are about the same (37 in or 94 cm to 39.4 in or 100 cm), only the height will

be factored in the analysis. The figure below shows the run-up reduction of the models

normalized by model height. It should be noted that the model height might not correlate with

62

run-up reduction proportionally. However, this is a better comparison than comparing just the

raw results.

Figure 5.2-3: PVC Model, Run-up Reduction Normalized by Model Height 5 degree

Figure 5.2-4: PVC Model, Run-up Reduction Normalized by Model Height 10 degree

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Generally, Angle L4 has the highest run-up reduction in both 10 and 5 degree. The other

three configurations are similar in terms of run-up reduction. In the 10 degree beach slope, the

downward trend of run-up reduction is clearer. In this setup (10 degree beach), the Angle L3 and

semi-circular L4 offers similar run-up reduction, while the semi-circular L1 having slightly less

run-up reduction.

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5.3 PVC model vs. Rectangular Models

In this section, the results of the PVC models were compared with the rectangular models

to determine the significances of geometry of the breakwater in run-up reduction. However, the

d/h ratio for the PVC models and the rectangular models are not the same. The angular PVC

model has a d/h of 0.54 and the circular PVC model has a d/h of 0.38 while the rectangular

model has a d/h of 0.30. From previous sections, it is clear that the PVC model performed better

than the rectangular models – however, whether this is due to the geometry is unknown since the

d/h of both PVC models is bigger than the rectangular models. To test the claim that the

geometric factor played a significant role in run-up reduction, experimental data from

Mohandie’s work was used. Figure 5.3-1 shows the run-up on a 5 degree beach slope with a

rectangular breakwater of d/h = 0.65 and L/h of 14.6 (close to one wavelength). Both the d/h and

the length of the rectangular model are bigger than the PVC models (while length of model is

still less than one wavelength). (R/h w/reef is the rectangular breakwater case, and R/h w/o reef

is the reference case.)

65

For comparison, the graph with the same scale was created for the PVC models. As

shown below, the run-ups are lower in the PVC models as compared to the rectangular model.

For the rectangular case, run-up soar above 0.2 with wave amplitudes between 0.05 and 0.1,

whereas for the PVC models, run-up does not reach above 0.2 until pass wave amplitude of 0.15.

At the higher end, for the rectangular model, the run-up is about 0.35-0.4 at amplitude slightly

below 0.2, whereas for the PVC model, run-up remained below 0.35 when amplitudes are close

to 0.2. Note that the rectangular model should have performed better with a higher d/h. This

means that the geometric factor in the PVC models significantly reduced run-up even with lower

d/h (and the length).

Figure 5.3-1:Experimental Results from Mohandie (2007); Rectangular Rigid model 5 degree slope; d/h of 0.65

66

Figure 5.3-2: Experimental results PVC model run-up; 5 degree slope

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5.4 Experimental Plastic Rectangular Model vs. Mohandie’s (2008) Numerical Results

Regarding Optimal Breakwater Length

In this section, Mohandie’s (2008) 5 degree beach slope numerical data was compared

with the experimental results obtained in this study. Figure 5.3-1 below shows the theoretical

results compared to the experimental results. The red and blue lines near top of the graph are

numerical results compared to the experiment results in teal, green and purple.

The magnitude of the reduction in the experiments is somehow smaller. The

experimental data resulted in a run-up reduction of 0-10%, whereas the numerical has a run-up

reduction of 15-35%. The trend of the two are similar in that they both increase in run-up

reduction and then reduce as the model length increases. The optimal point for the numerical

simulation is about 2 times the wavelength whereas the experimental data varied. The table

below details the estimation of the optimal run-up reduction model length by interpolation.

Figure 5.4-1: Numerical vs. Experimental Results Plastic Rectangular Models

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Table 5.4-1: Optimal Model Length based on Rectangular Plastic Models

Amplitude Range Model length (in terms of wavelengths)

0.16-0.18 1.30

0.20-0.23 1.25

0.24-0.26 1.91

At the higher amplitude range, the experimental data quantitatively resembles the

numerical trend. The data also agrees with the numerical results that the longer model lengths

are not always better. Although this trend is not as clear in the Foam models. The figure below

shows the numerical results compared to the experimental results. We should point out that the

numerical results were obtained for impermeable rectangular breakwater models, not foam

porous models.

Figure 5.4-2: Numerical vs. Experimental Results Foam Model

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The downward trend of run-up reduction as model length increase is not as clear.

However, with exception of the last data point in the amplitude of 0.24-0.26 range, the run-up

reduction is generally decreasing as the model length increases pass 2 times the wavelength.

Moreover, the numerical results are based on a rigid rectangular breakwater. This trend might

not apply to flexible breakwaters such as the foam model. The numerical results were only for a

5 degree beach slope and the 10 degree data was not compared.

Lastly, the run-up reduction tables for the PVC models are repeated here below. For

these models, the model length is all under one wavelength. Hence, the longer model (L2 and L4)

should have a better run-up reduction, since it did not reach the optimal point yet. Out of the 38

comparisons (non-zero) 34 of the 38 have a better run-up when the model is twice the length.

Table 5.4-2: Run-up Reduction for PVC Models (Highlighted means higher reduction for 2L model) 5 deg

Run-up Reduction Summary 5 degree

Amplitude Range Circular Angle

L1 L2 L3 L4

0.019 - 0.020 0.0% 0.0% 0.0% 0.0% 0.049 - 0.086 53.8% 48.0% 1.0% 47.9% 0.071 - 0.106 46.4% 29.2% 14.7% 57.3% 0.119 - 0.133 37.6% 43.4% 33.0% 52.4% 0.125 - 0.155 37.1% 22.4% 24.1% 42.5% 0.155 - 0.175 33.1% 23.3% 32.6% 43.4% 0.180 - 0.190 24.4% 25.0% 29.8% 45.4% 0.205 - 0.211 23.5% 20.9% 29.1% 44.5% 0.238 - 0.243 22.4% 26.5% 28.3% 45.5% 0.268 - 0.274 15.9% 25.6% 33.5% 46.0%

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Table 5.4-3 Run-up Reduction for PVC Models

(Highlighted means higher reduction for 2L model) 10 deg

Run-up Reduction Summary 10 degree

Amplitude Range Circular Angle

L1 L2 L3 L4

0.019 - 0.021 0.0% 32.1% 18.4% 55.8% 0.060 - 0.083 31.3% 44.7% 60.3% 71.1% 0.100 - 0.113 30.3% 41.9% 58.8% 67.0% 0.113 - 0.133 23.1% 32.7% 48.3% 60.8% 0.121 - 0.157 21.2% 32.2% 44.3% 50.5% 0.148 - 0.179 17.9% 18.1% 37.6% 54.0% 0.173 - 0.186 15.9% 20.5% 33.2% 45.0% 0.205 - 0.208 18.3% 18.5% 31.2% 36.5% 0.235 - 0.245 17.2% 19.3% 32.8% 48.2% 0.257 - 0.274 19.1% 21.7% 30.7% 46.3%

5.5 Rectangular Models 5 ft Breakwater Spacing Configuration

This section details the brief study of using the breakwater models with a spacing in

between. The purpose of this is to see if a better breakwater configuration can be found by using

the same amount of materials. In this study, the 5 feet rectangular models were compared to two

2.5 feet rectangular models with a 5 feet spacing in-between the two breakwaters as shown in the

figure below.

R

60”

β

x

WG1 WG2

α

h0

wavemaker

Figure 5.5-1: Normal Experimental Setup with 5 ft model used for comparison

1”

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Table 5.5-1 to Table 5.5-4 below show the results for the test runs for the foam and

plastic rectangular models at 5 and 10 degree beach slope. The measurements and run-up are

normalized by the water depth.

Table 5.5-1: Plastic Rectangle 5 ft with spacing (5 ft) 5 degree

Plastic Rectangle 5 ft with spacing (5 ft) 5 degree Amp Raw Measurement Run-Up 0.020 0.381 0.033 0.071 0.821 0.072 0.083 1.262 0.110 0.112 1.631 0.142 0.124 2.321 0.202 0.152 2.417 0.211 0.168 3.024 0.264 0.198 3.738 0.326 0.227 4.238 0.369 0.254 5.000 0.436

R

β

x

WG1 WG2

α

h0

wavemaker

Figure 5.5-2: Experimental Setup of breakwater model with spacing

1”

30” 30” 60”

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Table 5.5-2: Plastic Rectangle 5 ft with spacing (5 ft) 10 degree

Plastic Rectangle 5 ft with spacing (5 ft) 10 degree Amp Raw Measurement Run-Up 0.038 0.500 0.087 0.081 0.869 0.151 0.118 1.095 0.190 0.154 1.452 0.252 0.173 2.262 0.393 0.194 2.690 0.467 0.223 2.964 0.515 0.230 3.464 0.602 0.238 3.571 0.620 0.267 3.690 0.641

Table 5.5-3: Foam Rectangle 5 ft with spacing (5 ft) 5 degree

Foam Rectangle 5 ft with spacing (5 ft) 5 degree Amp Raw Measurement Run-Up 0.051 0.488 0.043 0.081 0.821 0.072 0.112 1.214 0.106 0.127 1.571 0.137 0.162 1.988 0.173 0.194 2.345 0.204 0.221 2.762 0.241 0.233 3.262 0.284 0.238 3.631 0.316 0.270 4.179 0.364

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Table 5.5-4: Foam Rectangle 5 ft with spacing (5 ft) 5 degree

Foam Rectangle 5 ft with spacing (5 ft) 10 degree Amp Raw Measurement Run-Up 0.032 0.274 0.048 0.040 0.524 0.091 0.067 0.893 0.155 0.089 1.155 0.201 0.131 1.440 0.250 0.160 1.714 0.298 0.167 2.167 0.376 0.207 2.381 0.413 0.237 2.643 0.459 0.256 2.917 0.506

Figure 5.5-3 to Figure 5.5-6 below compare the 5 feet breakwater models (in two 2.5

feet) with 5 feet spacing to their respective model and beach slope of the normal 5 feet

rectangular breakwater model.

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Figure 5.5-3: Plastic Model with spacing comparisons 5 degree

Figure 5.5-4: Foam Model with spacing comparison 5 degree

75



76

In the 5 degree beach slope, there are no significant differences between the 5 ft. and the

5 ft. with spacing models. However, in the 10 degree beach slope, a slight difference can be seen

between the two models. Moreover, the plastic and foam models behaved differently. The

model with spacing performed better in the plastic model whereas the model with no spacing

performed better in the foam model. Upon closer look in the 5 degree beach slope test runs,

although the difference is small, the two models also follow the same trend – for plastic model,

the model with spacing performed better, and for foam model the model with no spacing

performed better.

5.6 Errors and Accuracies

Errors are bound to exist in experimental studies. In this study, there are many different

equipment working together and many different measurements that are needed to be made. The

accuracies of the wavemaker and the wave gauges are described in a previous section in Chapter

3. The water level, and inundation are manually measured with a ruler with millimeter accuracy.

The beach slope is measured by Johnson Magnetic Angle Locator with at accuracy of 1 degree.

It is important to note that there is possibility of human error, as each data point required the

input of a new wave file into the computer, a manual split second measurement of the wave

inundation, and the exporting of the wave amplitude from the computer. These are all possible

errors that, although were minimized by following procedure, should be acknowledged.

In addition to the possible errors listed above, friction due to fluid viscosity and the

narrow flume size walls and flume bottom was not accounted for in the present analysis nor in

the numerical results based on the inviscid wave theory.

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CHAPTER 6 Conclusion

6.1 Summary of work and findings

The following are the findings of this study:

• Experimental results found that the rectangular plastic model did not have a significant

impact on run-up reduction.

• Experimental results strongly support that foam/flexible and porous material are better

than plastic/rigid and impermeable material for submerged breakwaters.

o The rectangular plastic models have a run-up reduction of around 0-20%.

o The rectangular foam models have a run-up reduction of around 25-50%.

• Experimental results in this study also showed that the saw-tooth shaped breakwater

model has a better effect in reducing the wave run-up, however, since the model height of

d/h = 0.58 is higher than the other models, the added reduction could be partially due to

the geometry and partially due to the increase in model height. This issue needs further

research by maintaining the same model height d/h in all the experiments in order to

single out the effect of breakwater geometry on wave run-up reduction.

o Further analysis by comparing the PVC angular and circular models to

rectangular models with a higher d/h show that the PVC angular and circular

models still has a better run-up reduction. It can be concluded the geometric

factor played a role in the run-up reduction.

• Experimental results generally agree qualitatively with the numerical simulation done by

Mohandie and Teng (2012) that an optimal breakwater length exists for run-up reduction.

78

o The rectangular plastic models follow the same trend as the numerical results of

increasing run-up reduction to a certain point than decreasing as the model length

increases. However, the magnitudes of the reduction are significantly different.

o The numerical results seems that the optimal breakwater length is two times the

wavelength whereas, the experimental data ranged from 1.25-2.00 times the

wavelength.

o The magnitudes of the run-up reduction % between the numerical and

experimental data are off by about 20%. This represents a magnitude difference

of over 2 times.

o The rectangular foam model very slightly follows the trend of the numerical

results. The difference may be due to the fact that the numerical results are based

on a rigid rectangular breakwater.

o Out of the 38 (non-zero) comparisons between model lengths of L1 vs. L2 and L3

vs. L4 for the circular and angular models, 34 of the 38 points have a better run-up

reduction for the longer model. For all the PVC models, the model lengths are

less than one times the wavelength.

• Experimental results for breakwater configurations with spacing for 5 degree beach slope

show no significant difference when compared to a breakwater model with no spacing.

• Experimental results for breakwater configuration with spacing for 10 degree beach slope

showed mixed results between the plastic and foam models. The plastic model showed

better run-up reduction for the breakwater with spacing and the foam model showed

better run-up reduction for the breakwater without spacing.

79

Based on the observations above, a rigid rectangular breakwater with a smooth surface is

not recommended. Although, the numerical studies has shown a higher run-up reduction for

these models – more work needs to be done to investigate this matter. Despite the significant

magnitude differences between the numerical and experimental studies, both agree that an

optimal breakwater length exist. Compared to rectangular plastic (rigid) model, the

rectangular foam model offers a significantly higher run-up reduction. Although a foam type

material may never be practical, the importance is the finding that the flexible, porous, and

rough surface was responsible for the increased run-up reduction. Lastly, this experimental

study has shown that breakwater models with saw-tooth geometry are better than rectangular

breakwaters. However, the degree of additional run-up reduction is not clear due to the

physical dimensional differences of the models in this study. Section 6.2 highlights several

recommendations that can be done to further investigate several issues found in this study.

6.2 Recommendations

For future studies, I would recommend the following:

• To better compare against numerical results, I recommend testing a finer range of

model length. In this study, a single model was tested over 10 different

amplitudes, which was useful in seeing run-up reduction over a large range of

amplitudes. However, when comparing model lengths, the data was lacking. I

suggest focusing on a few amplitudes and a larger/finer range of model length.

• This study has shown that a foam type material is better than rigid models as well

as using other geometry is better than a plain rectangular model. It will be

interesting to see the results for non-rectangular foam models.

80

o Furthermore, the reason for the better run-up reduction from the foam

model is not clear. Since the breakwater model is flexible, porous, and has

a rough surface as compared to the plastic rectangular model. An

experimental study to isolate and test each factor of the foam model would

be interesting.

• For this study, it was difficult to compare all the models due to different

parameters. I recommend using similar dimensions, (length and d/h).

• To further standardize procedures and to better compare results among different

studies, I recommend marking and recording equipment/breakwater locations.

• Lastly, to mitigate error and for better comparison of results, I recommend

repeating the trials runs. This will reduce errors and increase confidence in the

results. This will also created a standard of error in order to judge whether or not

the findings are significant or due to chance.

81

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