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CHAPTER 3

EXPERIMENTAL INVESTIGATIONS 3.1 GENERAL

Quantitative information on wave transmission, forces on the seawall and reflection

form the wall defenced by an offshore breakwater, is essential for performance

evaluation and design of the system. The flow becomes complex during wave

interaction with an offshore low-crested or submerged breakwater and seawall, which

makes the theoretical formulations to be difficult task. Due to the complexity of

specific formulations to understand and solve the problem, the physical model study

can be relied upon. The scaled down physical model represents a prototype system as

closely as possible following the Froude modeling. The purpose of physical model is

to approximate and anticipate the prototype behavior through prescribed modeling

laws. Physical modelling also provides insight into physical phenomena that could not

be fully understood otherwise. Hence a well controlled systematic experimental

investigation was carried out on seawall protected by an offshore low-crested

breakwater to understand the hydrodynamic performance of the combined system.

3.2 METHODOLOGY

The present experimental investigations were carried out to study the defensive

behavior of two defence structure configurations (i) the offshore low-crested rubble

mound and

(ii) semi-circular porous and non-porous breakwater under the action of regular

waves.

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The design of the experiments started from the selection of testing facility, fabrication

of models, selection of armour and core stones for the rubble mound breakwater,

selection of instrumentation and data acquisition system. The data collection was

followed by analysis of measured physical quantities to understand the phenomenon

under investigation. The experiments were conducted to fulfill the objectives of the

present study. The experimental set-up and data analysis procedures are presented in

the following sections. This chapter includes the details of testing facility, fabrication

of models, design wave parameters and data acquisition system.

The scheme of experiments were planned in three phases; first phase started with

measuring the wave forces on the conventional vertical wall (without defence low-

crested breakwater) for different water depths, wave amplitudes and frequencies of

regular waves.

These wave force data are required for (i) comparison with established theoretical or

semi-theoretical formulae such as Goda (1985) equation and (ii) non-dimensional

wave force ratio i.e., [Fxwb/Fxwob], where, Fxwb is the force measured on the vertical

wall in the presence of offshore low-crested breakwaters and Fxwob is the force

measured on the wall in the absence of low-crested offshore low-crested breakwaters.

Second phase started with construction of low-crested rubble mound breakwater

(LCRB) in front of vertical wall at a distance of Lpl (pool length, the space between

the breakwater and vertical wall). Tests were conducted for different water depths,

wave amplitudes and frequencies of regular waves. The physical parameters i.e.,

water surface elevations in the pool, wave forces on the vertical wall and the wave

reflections were measured using the wave probes and force transducers. Different

relative breakwater heights (h/d) were obtained by varying the water depths to

25

simulate the tidal fluctuations in the coastal environment. This procedure is repeated

for three different pool lengths i.e., 150mm, 350mm and 600mm and the resulting

physical parameters were measured. Two (0.40m and 0.60m) crest widths (B), and

seaside slope of 2H : 1V and 1.5H : 1V leeside slope were adopted in this study.

Some of the data for B=1.20m were carried out in the Department of Ocean

Engineering, IIT Madras, Chennai, India.

In this second phase, a similar procedure was followed by constructing a low-crested

rubble mound breakwater with a vertical face on the lee side (pool side) and 2H : 1V

slope on seaside.

In the third phase, a similar procedure was followed by constructing Semi-Circular

low-crested Breakwaters (SCLB) of radii 0.31m and 0.35m with four different

perforations of 0, 5, 10 and 15 percent. SCLB was chosen because of its many

inherent advantages. The radius was arrived based on the equal volume of

corresponding LCRB.

For all these above mentioned tests a constant bed slope of 1 : 35 was adopted in

flume as shown in sectional view of Fig.3.1. After processing the data obtained from

the tests the results were presented in the form graphs represented by different non-

dimensional parameters. These graphs were explained elaborately relating to its

physical phenomena in the real field situations and their physical significance. These

graphs also help the coastal engineers and designers in selecting a particular physical

parameter under a given range of environmental and structural conditions.

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3.2.1 Dimensional Analysis

The economic design of a stable coastal structure is a difficult problem involving the

complex interaction of waves and structure. Our lack of understanding has

concentrated our efforts observing macro-scale features of the processes in prototype

and in model, and attempting to link major parameters of the processes to stability and

response characteristics of the structure. There is no known mathematical equation

governing the behavior of rubble-mound structures when exposed to wave attack,

therefore, determination of correct similitude relationships must be done through

dimensional and inspectional analysis.

As a preliminary to planning the experiments and the presentation of the results, it is

useful to define the independent variables relating to the problem at hand, and

consider how these are related through a dimensional analysis. An outline of this

process in the context of wave structure interaction has been given by Sarpkaya and

Isaacson (1981). It is useful initially to list the dependent and independent variables

for the case of breakwater system.

The parameters considered in the interaction of waves and structures (low-crested

breakwater and vertical wall) are water depth d, incident wave height H, wave length

L, acceleration due to gravity g, velocity in the vicinity of cover layer v, linear

dimension of armor unit la, sea side slope angle with respect o horizontal α incident

wave angle β bottom slope seaward of the structure θ, dynamic viscosity µ,

characteristic linear dimension of armor unit surface roughness δ, mass density of

armor unit ρa, mass density of water in the vicinity of breakwater, ρw, wave run-up on

the impermeable vertical wall Ru, horizontal distance between the vertical wall and

low-crested breakwater Lpl, breakwater crest width B, Radius of the semi-circular

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breakwater R, permeability p, vertical distance between the still water level and

breakwater crest hc and height of the breakwater h. Assuming that all of these

important parameters, we can invoke the dimensional consideration to state that there

exists a function such that

),,,,,,,,,,,,,,,,,,,,,,( uLrtcplawa RKKKhhLRBplgdLHvf δµρρθβα (3.1)

The first six variables relate to the hydrodynamic forcing function (waves). The next

four variables are used to describe the armor unit`s buoyancy (or resistance to

gravity). The variables µ and δ are relate to viscous and friction forces respectively

and the remaining variables, except Kt, Kr , KL and Ru, are the parameters related to

structure geometry. The variables Kt, Kr , KL and Ru are the responses of the process.

One of the many possible combinations of the above parameters as a complete set of

dimensionless products was given as

HR

HK

HK

HK

LL

Hh

LR

LB

Hp

ll

gLLR

Ld

LH

dlf uLrtplc

a

w

aw

aa ,,,,,,,,,,,,,,,,,,,ρρδ

ρµυυθβα

(3.2)

HR

HK

HK

HK

LL

HhkRkB

Hp

ll

gLkdkH

dlf uLrtplc

a

w

aw

aa ,,,,,,,,,,,,,,,,,,ρρδ

ρµυυθβα

(3.3) The first six dimensionless parameters are related to geometrical undistorted model.

The seventh dimensionless parameter relates to armor layer Froude number. The

eighth dimensionless parameter relate to armor layer, Reynolds number and to satisfy

this condition the models should constructed at a large scale to assure that the flow

through the armor layer remains turbulent. The ninth dimensionless parameter relate

to the effects of surface roughness of armor layer. The resistance offered by surface

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roughness in prototype-scale armor is negligible. The term (ρa/ρw) states the relative

density relationship between armor material and the fluid in the prototype must be

maintained in the scale model. Term (√p/H) relates to the porosity and the incident

wave height and is negligible as the structure attains a dynamically stable position

with the time. The last four dimensionless parameters can be rearranged and the

expression becomes

HR

HK

HK

HKf uLrt ,,,

(3.4)

3.3 DESCRIPTIION OF THE MODEL

3.3.1 Vertical wall

The non-overtopping seawall model of 1180mm length, 500mm height was made of

12mm thick foam plastic sheet fixed to the closely braced rigid steel frame of mild

steel angles and channels.

3.3.2 Rubble Mound Breakwater

In the present investigation stability of the rubble mound breakwater was not the main

focus. A stable rubble mound breakwater with 2H:1V slope on seaside and 1.5H : 1V

on pool side, 1.50 - 2.0kg armour stone and 0.20-0.50 kg core stones was used. The

armour unit was designed using van der Meer (1987) formulae for plunging breaking

condition. Tests were conducted on rubble mound breakwaters of three configurations

with a crest width of 0.40m, 0.60m and 1.20m.

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3.3.3 Semi-circular Breakwater

Semi-circular porous and non-porous low-crested breakwaters were used in present

investigation. These models were fabricated with 3mm thick galvanized iron sheet

rolled into a semi-circular shape over a steel frame made of mild steel angles. Two

models of 0.31m and 0.35m radius were used. These radii were arrived by equivalent

volume of 0.40m and 0.6m trapezoidal rubble mound breakwaters of above

mentioned side slopes. The percentages of perforations adopted for the study are 0, 5,

10 and 15 percentage of the exposed area. The perforations were provided on both

sides of the semi-circular breakwater with circular openings.

3.4 TEST FACILITY

3.4.1 Wave Flume

The present experimental study was carried out in a 45m long, 1.2 m wide and 1.2m

deep wave flume in the Department of Civil Engineering, Andhra University College

of Engineering, Visakhapatnam, India (Photo 3.1). A schematic diagram of wave

flume, seawall model, breakwater, force balance and wave probes is presented in

Fig.3.1. The flume is capable of generating regular waves of different amplitudes and

frequencies. One end of the flume fitted with wave maker and the other end is

provided with a rubble wave absorber to absorb effectively the incident waves. The

water depth can be varied from 0.25 m to 0.80 m. A sloping flume bed of 1: 35 was

prepared with Galvanized iron sheets and slotted angle frames which allow the

adjustment of different of bed slopes. The model was fixed to the force balance as

shown in Fig 3.1 (photo 3.2) and placed at a distance of 30 m from the wave maker.

To measure the wave elevations, three wave gauges were placed on the seaward of the

offshore low-crested breakwater and one wave gauge was positioned in between the

low-crested breakwater and the wall. The position of seawall model and the

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perforated semi-circular breakwater model in the flume is shown in Photo 3.3. A

block diagram showing all the test conditions adopted for the present study is shown

in Fig.3.2.

3.4.2 Wave Generator

Within the mechanical, geometric and hydraulic limitations of the system, the wave

generating system is capable of generating different kinds of two-dimensional regular

sequence or sea state. The maximum water depth in the flume was limited to 0.80m

and the maximum amplitude is 0.22m.

3.5 INSTRUMENTATION

The personal computer is interface to data acquisition system for data collection from

two component force balance and capacitance type wave probes. Fig.3.3 shows the

schematic diagram of instrumentation set-up. A view of the instrumentation set-up

used for wave generation and data analysis is shown in Photo 3.4.

3.5.1 Wave Probe

The wave probe is a conductive type and consists of two concentric stainless steel

electrodes separated by Teflon windings. Electrodes measure the conductivity of the

instantaneous water volume when it is immersed. The conductivity is proportional to

the variation in the water surface elevation. A set of compensation electrodes mounted

at the bottom end of wave gauge to balance the influence of temperature or salinity

changes in the water. Two wave probes were used in the present work to measure the

incident wave height and wave height near model.

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3.5.2 Force Transducer

Wave forces on the model were measured using a strain gauge type two component

force balance. It measures the two components of forces in a rectangular co-ordinate

system. Measurement of the components (X, Z) is effected with the help of strain

gauge type force transducers. The transducers are of such a type that the

measurements are not influenced by fluctuations of the water pressure when waves

pass along the flume. The force balance consists of a stainless steel frame size 150mm

X 90mm X 90mm below which the force transducers are placed. The model was fixed

at the center of the force balance platform by using 10 mm stainless steel bolts.

In the direction of wave propagation, the X-force component is oriented.

Perpendicular to X-axis, the transducers to measure the components Z symmetrically

arranged. The balance was secured to a steel support set at the top of the flume and

rigidly fastened to the sidewalls of flume.

The force transducers were connected to a data acquisition system through carrier

frequency amplifiers. The sensitivity of the transducers at their rated loads is about ±

2mV/V, which means that, with standard amplifiers, even for much smaller forces

than the rated loads, the amplifiers can be set to give full scale indication.

3.6 EXPERIMENTAL PROCEDURE

3.6.1 Data Acquisition

The wave gauge signals acquired through amplifiers were filtered through a 20Hz low

pass filter. A dedicated personal computer was used for the generation of wave and

the simultaneous acquisition of signals from the sensor pickups. The instrumentation

set-up and closer view of the amplifier used for amplifying the signals from the

pressure transducers and force balance is shown are Fig.3.5. The physical quantities

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viz., water surface elevation, wave forces on the vertical wall were collected in the

form of electrical signals from respective wave probe and force balance. The

electrical signal was acquired by using quartz clock controlled 32-bit A/D (Analog to

Digital) converter. This A/D converter was supported by software that controlled the

sampling frequency of the data acquisition, number of data points to be acquired, total

time of data collection and data storage in the personal computer. The data was

collected at a rate of 40 samples per second.

3.7 DATA PROCESSING

The data collected was converted to physical variables by using the corresponding

calibration coefficients. The raw data was analyzed in time and frequency domain to

get a clear understanding of the phenomenon under investigation.

3.7.1 Regular Waves

The data acquisition was done with a sampling frequency of 0.025 sec and the length

of the record was for 100sec. The force and the wave elevation were acquired

simultaneously through a DAQ interfaced personal computer. The arrival time of

wave at the model depends on the wave frequency and water depth. The time history

was viewed on the monitor to verify the trend in its variation based on which the

starting and ending points of the time series for analysis were determined. Sufficient

time gap was allowed between successive runs to restore calm water condition in the

wave flume. The measured wave height and wave periods were obtained by analyzing

the measured time histories of wave surface elevation using threshold-crossing

analysis (Chakrabarti, 1985). The threshold crossing option is a generalization of the

classical zero-crossing analysis. For a pre-defined reference level, the input time

series channel is divided into events, each of which is defined by the time series value

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crossing the reference level in upward direction. For each event, the peak-peak value,

the minimum and maximum values, and the duration are determined, and stored in a

time series file. Wave synthesizer software was used for this purpose.

The time series of the different parameters stated earlier were viewed to pickup the

part of time series with regular trend by omitting the transient part. The regular time

series were then subjected to threshold crossing analysis to get the mean amplitude of

the time history. The mean of amplitude of measured hydrodynamic forces were

obtained using the above procedure for each test run.

In order to obtain the incident and reflected wave heights form the structure several

methods have been proposed to obtain the reflection coefficient of regular waves over

breakwaters. One method was proposed by Dean and Dalrymple (1991) and involves

traversing one wave probe in the direction of the wave propagation to measure the

maximum Hmax and minimum Hmin wave heights of the composite wave field. The

values of Hmax and Hmin correspond to wave heights at a quasi-antinode and node,

respectively, of the corresponding composite wave system. The incident wave height

HI is calculated as the average of Hmax and Hmin, and reflection wave height HR is

calculated as half the difference between Hmax and Hmin. Then the reflection

coefficient (Kt) was estimated as the ratio of reflected wave height HR to incident

wave height HI.

The analysis results and discussion in respect of wave forces and pressures on vertical

wall with and without offshore breakwater for different wave heights, wave periods,

crest elevations and for different water depth are presented in the chapter 4.

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Fig.3.1 Schematic diagram of experimental set-up of vertical wall and low-crested rubble mound breakwater system

SECTIONAL VIEW

Wave probes

Force Transducer

1 : 35

B

Vertical wall

Trolley

Lpl h hc

Wave maker

PLAN

wp

1.2

m

0.2m

1.1

8m

Wave absorber

45m

wave paddle

B

Lpl

0

wp

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Fig.3.2. Block diagram for the model testing programme showing different test parameters adopted in the present study.

Radius of the Semi-circular breakwater

h/d =0.66, 0.80 and 1.00

Lpl/h=7.5, 17.5 and 30

B=0.40 and 0.6m R=0.31 and 0.35m

Regular waves Regular waves

T=0.85-3.20s H=0.02-0.22m

R/Lpl=0.089, 0.10, 0.21 and 0.23

Constant breakwater height (h=0.20m)

h/d = 0.80 and 1.00

T=0.85-3.20s H=0.02-0.22m

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Fig. 3.3. Block diagram of instrumentation for measurements in the laboratory

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Photo 3.1 Experimental facility and positions of different models

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Vertical wall

Force Transducer

Transmission probe

Photo.3.2. Seawall model fixed with Two-component Force Transducer and position of transmission probe

Photo.3.3. Seawall model and position of perforated semi-circular breakwater

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Two-co

Two-component Force Transducer

Data Logger

Photo 3.4 Data Logger for wave probes and Force transducer with Data Acquisition system