Semicircular Breakwater Research Articles

Analytical and experimental studies on Bragg scattering of water waves by multiple submerged perforated semi-circular breakwaters

This study develops analytical solutions for Bragg scattering of water waves propagating over a series of submerged perforated semi-circular breakwaters (bars) based on potential theory. The series solutions for velocity potentials in the external common fluid domain of the bars are expressed through multipole expansions, whilst those in the internal fluid domains are given using the separation of variables. The continuous condition of fluid velocity and a quadratic pressure drop condition on the perforated semi-circular arcs are applied to determine the unknowns in the series solutions. In the analytical solutions, obliquely and normally incident waves are independently considered. The calculation methods of the reflection, transmission and energy loss coefficients are given. Experimental tests are performed to measure the reflection and transmission coefficients of the breakwaters at different wave periods and water depths. The analytical solutions are in excellent agreement with the independently developed multi-domain BEM (boundary element method) solutions, and are also compared with the wide-spacing approximations and the experimental results. Calculation examples are presented to check the effects of various parameters (e.g., bar number, bar radius, bar spacing and incident wave angle) on the hydrodynamic quantities of the breakwaters. Main valuable results for engineering application are draw.

Analysis of water wave interaction with a submerged quarter-circular breakwater using multipole method

This article studies water wave interaction with a submerged quarter-circular breakwater based on potential theory and multipole expansion method. The obliquely and normally incident waves are independently considered. The series solution of velocity potential in the external fluid domain is expressed through the multipole expansions, while the series solution of velocity potential in the quarter-circular internal fluid domain is obtained through the separation of variables. Then, the unknown coefficients in the series solutions are determined by matching the boundary conditions between external and internal fluid domains. The calculation methods for the reflection and transmission coefficients of the submerged quarter-circular breakwater as well as the horizontal and vertical wave forces on the breakwater are presented. The wave forces acting on the submerged breakwater with a seaside quarter-circular-arc and that with a leeside quarter-circular-arc are compared. The hydrodynamic quantities of the submerged quarter-circular breakwater are also compared with those of the submerged semi-circular breakwater. In addition, the effects of breakwater radius, incident frequency, and incident angle on the hydrodynamic quantities of the quarter-circular breakwater are clarified. Valuable results for practical engineering application are drawn.

Performance Assessment of a Semi-Circular Breakwater through CFD Modelling

Coastal defence works, such as breakwaters, are structures that aim to support the action of waves and dissipate their energy. Therefore, they provide conditions for stabilizing the coast, protecting ports, beaches and other coastal infrastructures and ecosystems. Semicircular breakwaters have been applied in different locations around the world due to their aesthetic advantages and high structural performance. Marine structures are subject to hydrodynamic actions normally estimated through physical models. However, these models are complex to implement, involving high costs and long experimental procedures. Thus, alternative methodologies for studying the hydrodynamic performance of these structures are of great use. This work presents the results of the application of a computational fluid dynamics (CFD) tool to study the stability of a perforated semicircular breakwater, based on a rubble mound foundation. The model was validated against experimental results of the critical weight necessary to resist sliding, taking into account the effects of water depth and different characteristics of the waves. A comparison is made between the perforated and the non-perforated solution in terms of the breakwater’s performance to dissipate wave energy. Dissipation conditions of this energy, in the exposed face, are also evaluated in detail, in order to assess the potential of this structure as a biological refuge for marine species. Both solutions show similar performance in terms of results obtained for the wave reflectivity coefficient. The turbulence dissipation on the exposed face of the perforated breakwater is limited to a region of restricted extension around it, which is advantageous in terms of the passage of species into the breakwater.

Iterative multipole solution for wave interaction with submerged partially perforated semi-circular breakwater

This study develops an iterative multipole solution for water wave interaction with a submerged partially perforated semi-circular breakwater based on the linear potential theory. Multipole expansion method and separation variable method are used for getting the velocity potential expressions of the flow fields, and the expansion coefficients in velocity potentials are determined by iteratively solving the non-linear pressure loss boundary condition on the partially perforated wall. The calculation results of the present multipole solution are in good agreement with the numerical results of multi-domain BEM (boundary element method) solution. The effects of the radius, porosity and perforated position on the reflection coefficient, transmission coefficient and wave force of breakwater are thoroughly discussed. Some meaningful suggestions are presented for engineering design.

Analysis of water wave interaction with a flexible submerged perforated semi-circular breakwater

Abstract This study examines the hydroelastic interaction between water waves and a flexible submerged perforated semi-circular breakwater based on linear potential theory. The breakwater is idealized as a bottom mounted perforated semi-circular Euler–Bernoulli beam with constant elasticity. The boundary condition on the flexible beam is derived from the equation of motion of the semi-circular beam, which is developed by the principle of virtual work. An analytical solution for wave interaction with the flexible breakwater is developed using multipole expansions. Also a numerical solution using multi-domain boundary element method (BEM) is developed for validation of the analytical solution, where the beam displacement is expressed as an integral representation involving unknown dynamic pressure difference between both sides of the beam using Green function technique. The convergence of the analytical solution is very rapid, and a few truncated terms yield results with five order of accuracy. Agreement between the analytical and numerical solutions is excellent. Features for hydrodynamic quantities of the flexible breakwater are examined by presenting typical calculation examples. Valuable results are drawn for engineering design of flexible structures.

Prediction of reflection coefficient of a perforated Quarter Circle Breakwater using artificial neural network (ann)

A breakwater is structure which is generally adopted in not only protecting the shoreline, but also in creating tranquil zone on the lee side of the structure minimizing the various movements on the anchored ships / vessels due to the wave / tidal action in the region resulting in easy handling of goods. Over the years, breakwater was generally constructed using rubble mounds. Due to the increase in demand for the coastal development all over the world, many innovative Breakwater were evolved as against the rubble mound. In the recent times, in order to economize the innovative breakwater construction, Semi Circular caisson type Breakwater has been studied. Based on Semi circularBreakwater (SBW), Quarter circular Breakwater (QBW) has been evolved. The hydrodynamic performance of a coastal structure is important, because it involves many parameters to be considered while designing a safe and economical structure. The hydro-dynamic performance of a Quarter circular breakwater is studied in a monochromatic wave flume in the Department of Applied Mechanics and Hydraulics, National Institute of Technology, Surathkal Karnataka, India. In the present paper reflection coefficient (Kr) of a perforated Quarter circular Breakwater (QBW) with various S/D ( spacing to diameter ratio) values is predicted applying Artificial Neural Network (ANN) technique using MATLAB. Four networks were constructed by varying the number of hidden layers based on the input parameters, which affects the performance of the breakwater. The predicted values of reflection coefficient using ANN, are compared with the experimental results.

Below the Data Range Prediction of Soft Computing Wave Reflection of Semicircular Breakwater

Coastal defenses such as the breakwaters are important structures to maintain the navigation conditions in a harbor. The estimation of their hydrodynamic characteristics is conventionally done using physical models, subjecting to higher costs and prolonged procedures. Soft computing methods prove to be useful tools, in cases where the data availability from physical models is limited. The present paper employs adaptive neuro-fuzzy inference system (ANFIS) and artificial neural network (ANN) models to the data obtained from physical model studies to develop a novel methodology to predict the reflection coefficient (Kr) of seaside perforated semicircular breakwaters under low wave heights, for which no physical model data is available. The prediction was done using the input parameters viz., incident wave height (Hi), wave period (T), center-to-center spacing of perforations (S), diameter of perforations (D), radius of semicircular caisson (R), water depth (d), and semicircular breakwater structure height (hs). The study shows the prediction below the available data range of wave heights is possible by ANFIS and ANN models. However, the ANFIS performed better with R2 = 0.9775 and the error reduced in comparison with the ANN model with R2 = 0.9751. Study includes conventional data segregation and prediction using ANN and ANFIS.

PSO-ANFIS hybrid approach for prediction of wave reflection coefficient for semicircular breakwater

ABSTRACT Breakwaters are used to provide protection to the coast and are being improved over the years through research. Semicircular breakwater (SBW) is one such contribution in the area of coastal structures with an improved esthetics and stability. Advances in artificial intelligence applications in several fields have led to the increased interest in the researchers of coastal engineering to venture into it. This paper focuses on the prediction of reflection coefficient (Kr ) for SBW using adaptive neuro-fuzzy inference system (ANFIS) and a hybrid of particle swarm optimization for adaptive neuro-fuzzy inference system (PSO-ANFIS) for a wide range of wave heights. The datasets required for the study are acquired from the experimental investigations of SBW in the regular wave flume at the Marine Structure Laboratory, National Institute of Technology Karnataka, India. The data fed for training and testing were taken in two forms separately, i.e. dimensional and dimensionless form. The PSO-ANFIS based optimized prediction of reflection coefficient is compared with the prediction arrived through ANFIS-based learning. The accuracy assessment of prediction was done by correlation coefficient, scatter index, Nash–Sutcliffe efficiency, bias, and root mean square error. The PSO-ANFIS hybrid model prediction improved the ANFIS prediction for the considered cases.

Tests on wave-induced dynamic response and instability of silty clay seabeds around a semi-circular breakwater

Model tests aimed at investigating the wave-induced dynamic response and instability of silty clay seabeds around a semi-circular breakwater were conducted in a large wave flume. The pattern of wave forces was measured and analysed. The seabed responses were presented in terms of pore pressure and vertical stress, which were further characterized in terms of their oscillatory and residual values. The wave-induced settlement and instability of the semi-circular breakwater were studied. Test results reveal that the total horizontal wave force was generally greater than the vertical wave force, and a phase difference existed in the total horizontal and vertical wave force patterns. The trends in the oscillatory pore pressure and vertical stress were very similar: they generally developed rapidly in the seabed on the wave side, tended to be larger in the upper silty clay and smaller in the bottom area and increased with increasing wave height. Furthermore, the oscillatory responses mostly reached stable states but were observed to vibrate with cyclic time in the destroyed silty clay. The residual pore pressure and vertical stress mainly developed in the seabed around the breakwater and could be quite different depending on the location. With the exception of the decrease-increase tendency in some seabed areas, the residual pore pressure generally increased with cyclic time beneath the breakwater. The residual vertical stress generally increased with cyclic time beneath the breakwater, except in some regions beneath the toes of the internal rubble bed. The semi-circular breakwater settled substantially into the silty clay seabed, and the settlement was greater on the wave side. This seabed shear failure is attributed to the strength degradation of the silty clay induced by the development of excess pore pressure and the destruction of the soil fabric.

Modeling of emerged semi-circular breakwater performance against solitary waves using SPH method

The semicircular breakwater (SBW) is a composite breakwater consisting of a hollow empty reinforced concrete caisson seated on the rubble mound breakwater. In this research, smoothed particle hydrodynamics (SPH) method was used to examine the run-up and overtopping of solitary waves on SBW. At first the SPH model was validated for regular wave–SBW interaction against experimental results. Comparisons showed that the present modified numerical model has a good agreement with experimental data. Parametric study was then performed on the effect of water depth and wave height of the single solitary waves and height of the rubble mound on wave run-up. Furthermore, double solitary waves were generated to study their interaction with SBW by the model. Run-up and reflection coefficient for double solitary wave–structure interaction was then investigated. The results show that in sum run-up in double solitary wave mode is smaller than that of single solitary wave. Moreover, the second solitary wave run-up is smaller than that of the first solitary wave in double solitary wave train. Overtopping discharge of double solitary wave is nearly constant for τ/T greater than 1.3, where τ/T is the ratio of time distance between wave crests of double wave to effective period of single solitary wave. Also overtopping discharge decreases with increasing in τ/T for its value smaller than 1.3. The results show that this model is a useful tool for simulating the interaction of solitary waves–structures with complicated geometry.

Comparison of Artificial Neural Network and Regression Approaches for Evaluation of Hydrodynamic Performance of Quarter Circular Break Water

Quarter-circle Break Water (QBW) is a modified semi-circular breakwater, which are similar to caisson consists of a quarter circular surface facing incident waves, with horizontal bottom and a rear vertical wall and are generally placed on a rubble mound foundation. QBW may be constructed as emerged with and without perforations that may be one side or on either sides. By these perforations, the energy is dissipated owing to the formation of eddies and turbulence is created inside the hollow chamber. In this paper, the data collected from the experimental work carried out at National Institute of Technology, Surathkal is analysed by plotting the non-dimensional graphs of reflection coefficient, reflected wave height and incident wave height for various values of wave steepness. These values are used for prediction of QBW adopting Artificial Neural Network (ANN) and Regression (REG) approaches. In ANN, Multi-Layer Perceptron (MLP) and Radial Basis Function networks are considered for training the network data. Goodness-of-Fit (GoF) test viz., Kolmogorov-Smirnov test statistic and Model Performance Analysis (MPA) viz., correlation coefficient, mean absolute error and model efficiency are applied for checking the adequacy of ANN and REG approaches to the observed data. The results of GoF test and MPA indicates the MLP is better suited for evaluation of hydrodynamic performance of QBW.

Wave Reflection and Loss Characteristics of an Emerged Quarter Circle Breakwater with Varying Seaside Perforations

Breakwaters are one of the most important harbour structures constructed to withstand and dissipate the dynamic energy due to the action of the waves. Due to fast growing need of the universe and advances in technology different types of breakwaters are being developed. Quarter circle breakwater is a new type of breakwater emerged from semi circular breakwater and the first model was developed in Peoples Republic of China (2006). Quarter circle breakwater with perforations posses merits of caisson as well as perforated breakwaters such as low weight, requires less materials, suited for poor soil conditions, easily transported, handled and placed at the site, aesthetically pleasing, cost effective, eco-friendly and stable. Therefore it is necessary to carry out detailed studies on hydrodynamic characteristics to investigate the suitability and applicability of various types of quarter circle breakwaters. The present study investigates the wave reflection and loss characteristics of an emerged seaside perforated quarter circle breakwater of radius 55 cm and with varying ratios of spacing to diameter of perforations, for different water depths and wave conditions. The tests were conducted in the two-dimensional monochromatic wave flume available in Marine Structures laboratory of Department of Applied Mechanics and Hydraulics of National Institute of Technology, Surathkal, Karnataka, India. The results were plotted as non-dimensional graphs and it was observed that the reflection coefficient increases with increase in wave steepness for all values of ratio of height of breakwater structure to water depth. For a constant water depth, wave reflection increases with increase in ratio of spacing to diameter of perforations. It was also found that the loss coefficient decreases with increase in wave steepness for all values of ratio of height of breakwater structure to water depth, and ratio of spacing to diameter of perforations.

Wave interaction with a submerged semicircular porous breakwater placed on a porous seabed

In the present study, a coupled eigenfunction expansion-boundary element method is developed and used to analyze the interaction of surface gravity waves with a submerged semicircular porous breakwater placed on a porous seabed in water of finite depth. Two separate cases: (a) wave scattering by the semicircular breakwater, and (b) wave trapping by the semicircular breakwater placed near a porous sloping seawall are studied. Further, as a special case, wave trapping by a semicircular breakwater placed on a rubble mound foundation near a sloping seawall is analyzed in water of uniform depth having an impermeable bed. The wave motion through the semicircular permeable arc of the breakwater is modeled using the Darcy's law of fine pore theory, whilst the wave motion through the porous seabed, rubble mound foundation and the porous seawall are modeled using the Sollitt and Cross model. The friction coefficient defined in Sollitt and Cross model is computed by approximating the spatial dependency of the seepage velocity with the average velocity within the porous media. An algorithm for determining the friction coefficient f is provided. Various physical quantities of interests are plotted and analyzed for various values of waves and structural parameters.

Wave load on submerged quarter-circular and semicircular breakwaters under irregular waves

Laboratory experiments were conducted to investigate the characteristics of wave loading on submerged circular-front breakwaters due to irregular waves. The wave force spectrum for a semicircular breakwater is similar to that for a quarter-circular breakwater. The dimensionless peak wave force for irregular waves is less than that for regular waves. The performance of our theoretical wave load model is improved significantly by incorporating the effect of wave transmission and flow separation. A RANS-VOF model was used to investigate the effect of local hydrodynamic disturbances by submerged breakwaters on the pressure distribution around the breakwater and total wave load. The numerical results reveal that wave-induced vortices at the structure have a substantial influence on the wave loading on the submerged quarter-circular breakwater but not on the semicircular breakwater. A parametric analysis is required to further improve the relationship between wave loads and the vortices.

Bragg reflection of water waves by multiple submerged semi-circular breakwaters

This study examines the Bragg reflection of water waves by multiple submerged semi-circular breakwaters. The multipole expansions combined with the shift of polar coordinates are used to develop full linear potential solutions of the problem. In the full solutions, the obliquely and normally incident waves are independently considered. Experimental tests are carried out to measure the reflection and transmission coefficients of the breakwaters at different wave periods and body spacings. The analytical results are in reasonable agreement with the experimental data. The peak reflection coefficient of multiple submerged semi-circular breakwaters and the bandwidth of Bragg reflection are carefully examined by numerical examples. Some significant results for practical application are discussed.

Stability of a Perforated Quarter Circle Breakwater

Many new types of breakwaters have been constructed of lateto fulfill the ever increasing demand of marine traffic. The quarter circle breakwater (QBW) is a recent type of breakwater developed on the lines of an earlier semicircular breakwater (SBW). QBW may be without perforations, seaside perforated or both sides perforated. A series of laboratory experiments were conducted in a two dimensional monochromatic wave flume on an emerged seaside perforated non-overtopping quarter circle breakwater model to study its stability against sliding. The scale of the model was 1:30. A range of incident wave heights (Hi) and wave periods (T) were generated in the flume simulating the wave climate off Mangaluru coast in the Karnataka State of India. The experimental data so collected was analyzed to understand the variation of the non-dimensional stability parameter with incident wave steepness for different values of dimensionless depth parameter In the end a nomogram was developed for computing the sliding stability of the breakwater.

Prediction of Hydrodynamic Characteristics of Quarter Circular Breakwater Using Stepwise Regression

Quarter Circular Breakwater (QBW) is emerging as a new topic of research for port engineers worldwide, with a special emphasis on its hydrodynamic performance characteristics. QBW is a new type of breakwater based on the principles of Semicircular breakwater (SBW). The present paper discusses the development of prediction models for the coefficient of transmission of QBW using MATLAB based stepwise regression approach. Data used for the modeling was obtained from experiments conducted on scaled downed physical models of QBW in the regular wave flume available at the Marine Structures laboratory of the Department of Applied Mechanics and Hydraulics, National Institute of Technology Karnataka (NITK), Surathkal in India. Using the stepwise method to perform a multi-linear regression of the transmission coefficient (Kt), a relation was established in terms of independent parameters such as wave height (H), wave period (T) and depth of water (d).

Runup and Rundown Characteristics of an Emerged Seaside Perforated Quarter Circle Breakwater

Quarter circle breakwater (QBW) is developed from semicircular breakwater (SBW) and the first model was developed in Peoples Republic of China. The superstructure of QBW consists of a quarter circular front wall facing incident waves, a horizontal base slab and a vertical rear wall placed on rubble mound foundation. A series of experiments were conducted in a two dimensional regular wave flume available in Marine structures laboratory of Department of Applied Mechanics and Hydraulics of National Institute of Technology, Surathkal, Karnataka to assess the wave runup and wave rundown characteristics of an emerged seaside perforated quarter circle breakwater. Quarter-circle breakwater models with three different radii and S/D (spacing to diameter of perforations) ratio equal to 5 were tested. The data collected was analyzed by plotting the graph of dimensionless wave run up, Ru/Hi (where Ru= runup and Hi= incident wave height) and dimensionless wave rundown, Rd/ Hi (where Rd = wave rundown and Hi= incident wave height) for various values of wave steepness, Hi/gT2 and different height of structure to the depth of water (hs/d) values. The dimensionless wave runup, Ru/Hi increases with the increase in the wave steepness and also it increases with the increase in hs/d but the dimensionless wave rundown, Rd/Hi decreases with the increase in the wave steepness and also it decreases with the increase in hs/d.

Transmission Performance of Submerged Semicircular Breakwaters for Different Radii and Submergence Ratios

The paper presents the results of a series of laboratory experiments that were conducted in a 2D monochromatic wave flume of the department to evaluate the transmission characteristics of scaled down semicircular breakwater (SBW) physical models of different radii (R) for different submergence ratios (d/hc), where d is the depth of water and hc is the height of the breakwater crest from the sea bed. The radii of the breakwater models studied were 20 cm, 22.5 cm, 25 cm, and 27.5 cm and d/hc values used varied from 1.067 to 1.667. The wave climate along the Mangalore coast of India was used for arriving at the various wave parameters. Incident wave heights (Hi) used varied from 3 to 18 cm, wave periods (T) ranged from 1.2 s to 2.2 s with water depths (d) of 40 cm, 45 cm and 50 cm. The data collected was analyzed by plotting the non-dimensional graphs depicting the variation of transmission coefficient Kt (Kt = Ht/Hi, where Ht = transmitted wave height) with wave steepness Hi/gT2 for different R/Hi and d/hc values. It was found that transmission coefficient decreased as the incident wave steepness increased for different submergence ratios. Also as d/hc increased, it was found that Kt increased initially and then decreased.

Quarter Circular Breakwater: Prediction of Transmission Using Multiple Regression and Artificial Neural Network

AbstractThe physical model study of coastal structures is a nonlinear process influenced by innumerable parameters. As a result of a lack of definite systems, intricacies, and high costs involved in the physical models, we need a simple mathematical tool to predict wave transmission through quarter circular breakwater (QBW). QBW is a state-of-the-art breakwater essentially based on the exploitation of the concepts of semicircular breakwater. This paper discusses the use of soft computing tools such as MATLAB-based multiple regression (MR) and artificial neural network (ANN) to predict the wave transmission coefficient of QBW. To assess the accuracy of the proposed model and its ability to forecast, correlation coefficient and mean squared error are availed. On comparing the results obtained from MR and ANN, it is concluded that ANN gives more accurate results and can be used as a powerful tool for the modeling of hydrodynamic breakwater transmission through QBW. It serves as a viable alternative to the conventional physical model to simulate the hydrodynamic transmission performance of QBW.