Study on the hydraulic stability and structural integrity of randomly - Placed rakuna - IV on rubble mound breakwaters

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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