Within the scope of the study, the calculation results show that the block weight

determined by the empirically derive formula for hydraulic stability is greater

than that calculated by Hudson’s formula due to the consideration of more

parameters and the rocking mechanism, thereby tending towards the safety of the

structure in terms of both hydraulic stability and structural integrity under the

impacts of incoming waves (see Table 4.6 and Table 4.9).

In addition, it can be seen that the block weight is much smaller in case the

empirical formula without considering the effect of rocking mechanism is used.

The calculation then tends towards economical purposes, but may not ensure the

hydraulic stability and structural integrity of the concrete armour units (see Table

4.8)

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previous studies
on the hydraulic stability of RAKUNA-IV armour units but only focused on the
case of regular placement on seaward slope of rubble mound breakwaters and
there have been no studies on the hydraulic stability as well as the structural
integrity of randomly-placed RAKUNA-IV armour units. This is a practical and
urgent problem where in most cases (especially in deep-water areas), the concrete
armour units are commonly placed in random patterns.
1.2 Overview of hydraulic stability of concrete armour units
1.2.1 General introduction
So far, there have been a large number of empirical formulae derived from many
studies on the hydraulic stability of armour units on the slopes of rubble mound
breakwater conducted by Tyrel (1949), Mathews (1951), Rodolf (1951),
Iribarren and Nogales (1950), Larras (1952), Hedar (1953), etc. Based on the
consideration of the balance of forces, many scientists have determined the
formulae for hydraulic stability of the armour units on the slope, such as Iribarren
(1938), Iribarren and Nogales (1954), Hudson (1958, 1959), Svee formula
5
(1962). Since then, a series of studies on the stability of armour units on seaward
slope of rubble mound breakwater have been conducted and developed with
various derived formulae such as Tyrel (1949), Mathews (1951), Rodolf (1951),
Iribarren and Nogales (1950). ), Larras (1952), Hedar (1953) etc.
1.2.2 Studies on hydraulic stability of concrete armour units
Hudson (1959) proposed a formula for the hydraulic stability of a rock under the
impacts of incoming waves based on Iribarren's original formula. This formula
was generalized later so that it could be applied to various types of armour units
(rock and concrete blocks) under random wave conditions, in which the size of
armour units is indicated by the nominal diameter Dn.
Based on the results from many physical model experiments in Delft Hydraulics,
Van der Meer (1988) proposed a more general formula for 2-layer Tetrapods
placed on a slope of 1/1.5 under the impacts of non-breaking and non-
overtopping waves. Van der Meer, J.W. and Heydra, G. (1991) incorporated the
rocking mechanism into the hydraulic stability of Tetrapod armour units, and
concluded that the instability due to rocking occurs mostly in the area around the
design water level. These test results can be used to calculate the maximum
stresses in the concrete armour units and the number of blocks with breakage,
including the possible distribution of loading conditions, internal stresses of the
concrete armour units and the effect of resulting collision on the tensile strength
of concrete. These testing and measurement methods are the complement to the
method proposed by Burcharth and Howell (1988) in order to directly measure
the stresses in the concrete armour units.
For RAKUNA-IV armour units, Mase, H., Yasuda, T., Mori, N., Matsushita, H.
and Reis, M.T. (2011) conducted studies on hydraulic stability of horizontally
composite breakwaters, taking into consideration the effects of wave steepness
and wave breaking, with a foreshore slope of 1/30, 1/15 and a horizontal bottom
(with a constant water depth). Based on the analysis of the research results on the
application of RAKUNA-IV armour units to a two-layer slope of rubble mound
6
breakwater under non-overtopping wave conditions, which was conducted in the
wave flume at Thuyloi University (formerly Water Resource University) in 2010,
Tuan et al. showed that in the initial state, RAKUNA-IV armour unit is about 1.6
times more stable than Tetrapod. Tuan et al. (2012) also derived a formula for
the hydraulic stability of RAKUNA-IV armour units, with a similar form to that
for Tetrapods introduced by Van der Meer (1998) by means of regression
analysis based on the experimental data. Suh, Kyung-Duck & Hoon Lee, Tae &
Matsushita, Hiroshi & Ki Nam, Hong (2013) conducted model experiments for
different wave conditions and seaward slope in order to establish stability
formulae for RAKUNA-IV armour units on rubble mound breakwaters.
Based on the results of the physical modelling experiments, Giang (2015)
investigated the hydraulic stability of RAKUNA-IV armour units under the
impacts of overtopping waves and the overtopping reduction feature which varies
according to the interactive nature of the waves on the seaward slope of rubble
mound breakwaters. The combination of a physical wave flume and a digital gave
a significant insight into the physical nature of the water-cushioning effect, which
governs the overtopping reduction feature of RAKUNA-IV armour units, and
also an empirical formula was derived in order to determine the level of the
stabiliy increasing level in case of overtopping waves in the form of increased
stability factor and the overtopping reduction coefficient.
1.3 Overview of structural integrity of concrete armour units
1.3.1 General introduction
Slender, complex types of armour units such as Tetrapods and Dolosse have been
widely used for rubble mound breakwaters. The breakage of these armor units
has caused many failures to rubble mound breakwaters, therefore the need for
studying stresses in concrete armour units under wave impacts has been fully
recognized. The stability of the armour layer will decrease if the concrete armour
units are broken and as a result will reduce the interlocking efficiency. Moreover,
the debris from broken armour units may be thrown due to wave actions and may
7
increase the damage caused by cracks. In order to reduce cracking, it is necessary
to ensure the structural integrity of concrete armour units.
1.3.2 Studies on structural integrity of concrete armour units
There have been many studies on experimental models built to measure stresses
in Tetrapods and Dolosse armour units under wave impacts by means of
mounting stress-strain gauges. Typical studies were those of Burcharth (1980,
1981, 1983, 1986, 1988, 1990, 1991, 1993, 1994), Van de Meer (1990, 1991),
Angremond (1994), Howell (1988), Ligteringen (1985) ), Nishigori (1986),
Terao (1982) and many others.
Many of the recent serious failures of rubble mound breakwaters protected by
Dolosse and Tetrapods armour units were caused by the cracking. The breakage
occurs before the hydraulic stability of the concrete armour units is no longer
maintained. Therefore, there exists an imbalance between the strength (structural
integrity) of the concrete armour units and the hydraulic stability (resistance to
displacement) of the armour layer.
H. F. Burcharth, G. L. Howell and Z. Liu (1991) conducted many experiments
on the prototype and small-scale physical models, providing the research results
for Dolosse armour units. Dolosse armour units were selected for the study due
to their high hydraulic stability and the fact that their structural integrity can be
adjusted by varying the waist ratio, in other words, the ratio between the diameter
of the fluke and the height of the unit. By increasing the waist ratio to achieve
greater durability, the hydraulic stability will be reduced to a certain extent,
which is a matter of design consideration. H.F.Burcharth, Liu Zhou, Gary L.
Howell, W.G.McDougal, (1991) presented the research and analysis results for
the experiments on the model of Dolos armour units by means of load-cell
techniques. Based on the results of studies on instrumented small scale model of
concrete armour units, Burcharth (1993b), Burcharth and Liu (1995); Burcharth
et al. (1995b) also derived an empirical formula to estimate the relative cracking
8
level of Dolos and Tetrapod armour units (in proportion to the total number of
blocks).
The insertion of the load-cell destroys the homogeneity of the material. This
means that the impact stresses recorded in the small scale model tests cannot be
scaled up to prototypes by the use of conventional formulae, which are valid only
for homogeneous material. This is only possible by determining the apparent
elasticity for the instrumented small scale models of the concrete armour unit,
which is used for the interpretation of the impact signals recorded in the wave
flume tests.
1.4 Conclusions for Chapter 1
Nowadays, the applicable conditions of rubble mound breakwaters are
increasingly expanded together with the invention and development of various
types of modified concrete armour units, with better efficiency in wave
attenuation and thus better economic performance. RAKUNA-IV is one of the
new types of concrete armour units that has been studied and developed by
Nikken Kogaku company since 2007 with many outstanding features and higher
economic efficiency than that of traditional concrete armour units such as
Tetrapods.
There have been a number of previous studies on the hydraulic stability of
RAKUNA-IV armour units but only focused on stability in case of reglular
placement on seaward slope of rubble mound breakwater, but there have been no
studies on the stability of this type of armour unit in case of random placement
on the seaward slope, especially the structural integrity under the impacts of
incoming waves. This is an urgent practical issue when in most cases (especially
at the breakwater head with great water depth) the concrete blocks for
breakwaters are usually placed randomly during construction, therefore the
armour units are easily subject to rocking movements under the action of waves
or currents resulting in the collision and generating stresses that can lead to
cracks, breakage and failures of these armour units.
9
CHAPTER 2 SCIENTIFIC BASES FOR THE STUDY ON
HYDRAULIC STABILITY AND STRUCTURAL INTEGRITY OF
CONCRETE ARMOUR UNITS ON RUBBLE MOUND BREAKWATERS
2.1 Overview of the experiments on hydraulic stability and structural
integrity of concrete armour units on the seaward slope of rubble mound
breakwaters
2.1.1 Stability and damage level of the concrete armour units on rubble
mound breakwaters
Damage to the armour layer of a rubble mound breakwater can be described as
the percentage of displaced units within a given area (may be all or part of the
armour layer).
- Relative damage level (D): Percentage of damage or the relative number of
displaced units within the reference area;
- The damage level according to the relative number of displaced units (Nod):
calculated by means of determining the number of displaced units after each
experiment.
In the study of hydraulic stability of RAKUNA-IV armour units, the relative
damage level (D) was used to determine the stability coefficient KD in Hudson's
formula, and the damage level according to the number of displaced units (Nod)
was used to derive an empirical formula in the form of non-dimensional stability
parameter Ns under the impacts of non-overtopping and non-breaking waves.
2.1.2 Determination of stresses by means of instrumented small scale model
of the armour units
Stresses in the instrumented models of RAKUNA-IV armour units can be
measured and determined by means of strain gauges mounted on the load-cells
inside the models. These strain gauges were carefully arranged so that the
induced strains can be measured and thereby deriving the corresponding stresses.
The parameter to be measured and determined is the increased impact stress
taking into account the rocking movements induced by incoming waves.
10
2.2 Dimensional analysis and basic governing parameters
The general function indicating the influence of the parameters on the hydraulic
stability of the armour units under non-overtopping and non-breaking wave
conditions is as follows:
The general function indicating the influence of the parameters on the structural
integrity of the armour units under non-overtopping and non-breaking wave
conditions is as follows:
2.3 Physical model setup for the studies on hydraulic stability and structural
integrity of RAKUNA-IV armour units on rubble mound breakwaters
2.3.1 Determination of the model scales
The scale effects on the model of the breakwater core can be overcome by
increasing the size of the stones in the model compared to that determined by the
model scale, by means of the method proposed by Le Méhauté. (1965) and
Keulegan (1973) in order to determine the material sizes for the underlayers and
the core of rubble mound structure models so that wave transmission is in proper
similitude.
For structural integrity tests, due to the two different scaling laws for non-impact
and impact stresses, it is necessary to separate the stress signal into an impact
portion and a non-impact portion, the latter including static and pulsating stresses
(Burcharth, 1993). The stress peaks can be transformed to the surface of the
prototype of RAKUNA-IV armour unit, so that the structural integrity can be
investigated and assessed.
2.3.2 Model design and experimental setup
2.3.2.1 Physical model setup
11
The experimental breakwater model consists of 3 layers: the armour layer
(covering layer), the underlayer and the core. The sizes of the armour layer and
the underlayer was scaled using the model length scale (according to the Froude’s
criteria). The model of RAKUNA-IV armour unit has a nominal diameter Dn of
6.7 cm with an average weight of 691 g and porosity of 56.5%. For the test series
on structural integrity, the instrumented models of RAKUNA-IV armour unit
were specially fabricated, which is basically composed of 03 parts: the concrete
lower body, the aluminum cylinder with wired strain gauges and the aluminum
upper leg drilled with a cylindrical hole.
Figure 2.7 Breakwater cross-section and physical model setup in wave flume
2.3.2.2 Mathematical model setup
In addition to the physical modelling experiments in wave flume, the study also
incorporated the ANSYS Mechanical APDL mathematical model in order to
simulate the intact model and the load-cell instrumented model of RAKUNA-IV
armour units.
Figure 2.12 Computing model setup with a finite element grid for the intact
model and the instrumented model of RAKUNA-IV armour units
12
In order to avoid the resonance or dynamic amplification, the natural frequency
of the instrumented model units should be smaller than the applied sampling
frequency. By means of Modal Analysis module in ANSYS Mechanial APDL
model, the natural frequency of the instrumented model units was determined as
f = 1727 Hz, which is much smaller than the applied sampling frequency f = 5000
Hz, thereby ensuring the accuracy and reliability of the experimental data on
structural integrity of RAKUNA-IV armour units.
2.3.2.3 Determination of conversion factor for the measured stresses
In order to determine the conversion factor for the experimentally measured data,
additional experiments using standard beam equipment with mounted FLA-5
strain gauges and HBM DMD 20A strain-meter were conducted in the Structural
Mechanics and Strength of Materials Laboratory at Thuyloi University. The
conversion factor was determined as 1 mV (of voltage increment) = 10-6 (of
induced strain). With the elastic modulus of aluminum material used for the load-
cell En = 7x1010 N/m2 = 70000 MPa, the conversion factor between the measured
voltage signal and the corresponding stresses is 1mV = 70 KPa or 1V = 70 MPa.
2.4 Conclusions for Chapter 2
Chapter 2 of the disseration presented the analysis of the governing parameters
as well as the construction of physical models in the wave flume in accordance
with Froude’s criteria in terms of kinetics and dynamics of wave parameters, as
well as the parameters related to length, area, volume, and mathematical model
setup for the research. In order to build the physical models and to set up the
mathematical models, the author applied Buckingham dimensional analysis in
order to determine the relationship between governing parameters as a basis for
constructing test scenarios on physical and mathematical models.
13
CHAPTER 3 RESULTS OF THE STUDY ON HYDRAULIC
STABILITY AND STRUCTURAL INTEGRITY OF RAKUNA-IV
ARMOUR UNITS
3.1 Study on the hydraulic stability of RAKUNA-IV armour units
3.1.1 Determination of stability coefficient KD from experimental results
Stability coefficient KD can be determined by formula (3-7):
where, Hs, D is the wave height corresponding to the design damage level D = 5%,
which is Hs, D = 0.165m cccording to the results of the experimental data analysis
above.
The experimentally derived stability coefficient of randomly-placed RAKUNA-
IV armour units under the impacts of non-overtopping and non-breaking waves
is KD = 10.6. It can be seen that this value approximately equals to that in case of
regular placement given in the current technical standards (KD = 10.8).
3.1.2 Deriving the formula for hydraulic stability in the form of stability
paramater Ns
The formula for hydraulic stability of RAKUNA-IV armour units is based on
stability parameter Ns and has the same form as that introduced by Van der Meer
for Tetrapods taking into account the rocking mechanism. The stability for
randomly-placed RAKUNA-IV armour units on a 2-layer slope of rubble mound
breakwaters under the impacts of non-overtopping and non-breaking waves can
be assessed by the formula (3-10) as follows:
The relationship between the two non-dimensional parameters can be determined
by means of regression analysis, from which the coefficients were determined as
4.47 and 0.85, respectively, and the data points located within the 95%
confidence limits (see Figure 3.9).
14
Figure 3.9 Regression analysis for all cases of incoming wave numbers Nz
3.2 Study on structural integrity of RAKUNA-IV armour units
3.2.1 Deriving the empirical formula for the impact stresses in the armour
unit model due to rocking movements under the impact of waves
The impact stresses generated in the armour units depend mainly on the stability
parameters (Ns) and wave parameters (Hs, s0m). From the results of studies on the
relationship between impact stresses due to rocking mechanism and the wave
height as well as the wave steepness, non-dimensional parameters can be
determined and included in the regression analysis using MatLab in order to
derive the empirical formula for the most critical impact stress in the
experimental models.
The regression analysis yields a correlation coefficient of approximately 0.85,
therefore an empirical formula was derived as follows (formula 3-13):
15
Figure 3.13 Regression analysis to derive the empirical formula for the critical
impact stresses in RAKUNA-IV armour units
It can be seen that the impact stresses in the rocking armour units under direct
wave impacts depend on the incoming wave parameters (wave height, wave
steepness) and the specifications of the armour units (size, density). From this, it
is possible to calculate the total stresses at the most critical section of RAKUNA-
IV armour units, and comparison and evaluation can be made based on the
current standards of allowable tensile strength of concrete in order to ensure the
structural integrity of the units.
3.2.2 Determination of apparent modulus of elasticity (Ea) and
corresponding scale factor (nE)
The scaling law for the impact stresses of armour units is related to the elasticity
of the material. However, the introduction of the load-cell destroys the
homogeneity of the model material. Therefore, it is necessary to determine the
apparent elasticity for the instrumented models using ANSYS Mechanical APDL
software.
From the results of simulations using ANSYS Mechanical APDL, the apparent
modulus of elasticity was determined as Ea = 5400 MPa, thereby giving the
corresponding scale factor of elastic modulus as nE = 4.5. By substituing this
16
value into the formula (2-27), the total stresses generated on the prototype
RAKUNA-IV block can be determined.
Figure 3.14 Simulation of stresses in the instrumented models of RAKUNA-IV
armour units by means of ANSYS Mechanical APDL
From the results of this study, it is possible to determine the most critical stresses
on the surface of concrete armour units under certain wave conditions and to
investigate and assess the breakage or damage of the concrete armour units
according to the national standard TCVN 5574: 2012 (Concrete structure and
Reinforced concrete - Design standards), thereby deriving the maximum
allowable weight of the concrete armour units without reinforcement.
3.3 Conclusions for Chapter 3
Chapter 3 of the dissertation presents the results of experimental data analysis
and proposes empirical coefficients as well as formulae for the hydraulic stability
and structural integrity of RAKUNA-IV armour units randomly placed on
seaward slope of rubble mound breakwater. Within the scope of the study
presented in this dissertation, the author established a series of experiments on
physical models in combination with finite element mathematical models to
study
17
(1) Hydraulic stability: determining the experimental stability coefficient KD =
10.6; establishing the empirical formula for RAKUNA-IV armour units within
the scope of the study;
(2) Structural integrity: establishing an empirical formula for the impact stresses
on the surface of RAKUNA-IV armour units subject to rocking under direct
impacts of incoming waves; investigating and evaluating the structural integrity
of the units based on the existing standards.
18
CHAPTER 4 APPLICATION OF THE RESEARCH RESULTS TO THE
DESIGN OF ARMOUR LAYER OF CHAN MAY BREAKWATER IN
THUA THIEN HUE PROVINCE
4.1 General introduction to the study area
Chan May Port is located in Chan May Bay (also known as Canh Duong Bay) in
Loc Vinh commune, Phu Loc district, Thua Thien Hue province, 49 km southeast
of Hue city center, about 5 km away from 1A national highway and the railway.
The center of the bay has the geographical coordinates of about 16°20'00"N -
108°00'00"E.
Chan May port is of economic and military importance, besides it has an
important infrastructure system and road transport system of the East-West
transport route passing through, services supplying electricity and water,
communication system for Chan May - Lang Co economic zone. Chan May Port
is located in the territory of Thua Thien - Hue Province, the gateway to the nearest
South China Sea, most convenient for the regions of the East-West Economic
Corridor. This is the main port between the sea route connecting Singapore, the
Philippines and Hong Kong. In addition, Chan May port is located in the central
position of Vietnam, between the two largest cities in Central Vietnam, Hue and
Da Nang. Therefore, Chan May has great advantages and potential in
international shipping and transshipment.
4.2 Design boundary conditions
(1) Deep water wave parameters: H0 = 8.4m; Tp = 11,2s; L0 = 195.69m
(2) Design wave parameters: Hs = 5.45m; Tm = 9.74s;
Lm = 147,97m; s0m = 0,037;
The design plan of the study area and the design cross-section of Chan May
breakwater are shown in Figure 4.3 and Figure 4.4.
19
Figure 4.2 Design plan of Chan May port
Figure 4.3 Design cross-section of Chan May breakwater
4.3 Design of the armour layer for Chan May breakwater
In the design of the armour layer of the Chan May breakwater, two types of
concrete armour units used for the purpose of analysis and comparison were
Tetrapods (traditional armour unit) and RAKUNA-IV (the subject of this study)
with the same boundary conditions (i.e. non-breaking and non-overtopping
waves). Here the dimensions of the applied armour units were calculated on the
basis of ensuring hydraulic stability by means of the two formulae:
20
(1) Hudson formula with KD stability coefficient:
This is a traditional formula to calculate the dimensions of concrete armour units
based on hydraulic stability on seaward slope of rubble mound breakwater.
(2) Empirical formula in the form of stability paramter Ns:
The stability of the armour units is considered in 2 cases: with and without the
effects of rocking mechanism.
Table 4.1 Alternatives for the design and comparison of concrete armour units
Alternative 1 Alternative 2
- Block: TETRAPOD;
- Regular placement, 2 layers;
- Slope factor: 1/1,5
- Applicable conditions:
non-overtopping, non-breaking waves;
- Loại khối: RAKUNA-IV
- Random placement, 2 layers;
- Slope factor: 1/1,5
- Applicable conditions:
non-overtopping, non-breaking waves;
Within the scope of the studies, the following criteria have been applied for the
analysis and evaluation:
(1) Dim

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