Permeable Breakwater Research Articles

A three-dimensional model of wave interactions with permeable structures using the lattice Boltzmann method

To simulate the three-dimensional interaction of waves and porous structures using the lattice Boltzmann method, a novel multi-relaxation-time lattice Boltzmann scheme corresponding to the volume-averaged Navier-Stokes equations incorporating porous flow is developed. The porosity is introduced into the equilibrium distribution function, and the frictional forces produced by the porous media are added by the discrete force model. Through the Maxwell iteration, the relation between the mesoscopic lattice Boltzmann scheme and the macroscopic governing equations is established. Large eddy simulation and the single-phase volume-of-fluid techniques are modified to take porous media into account. The friction parameters in this model are calibrated using the experimental data of two-dimensional dam-break waves interacting with porous media composed of crushed rocks. Validations are carried out by comparing the simulation result of the proposed model with the laboratory data of three-dimensional dam-break waves impacting a prism and three-dimensional surface gravity waves (solitary waves and cnoidal waves) interacting with a vertical permeable breakwater. Furthermore, the interaction of regular waves and a rubble mound breakwater is used to test the capability of the model to handle spatially varying porous media. The different simulation results strongly agree with the experimental data, which prove that the lattice Boltzmann model has the ability to simulate complex wave motions near porous structures.

Moored ship motion under the resonance conditions with breakwaters: A coupled numerical approach

A hybrid element model has been formulated to understand the wave interaction with moored ship motion using mild slope equation (MSE) including the influence of breakwaters and wave absorbers, under resonance conditions for variable bathymetry. In a hybrid element formulation, a combined approach with the finite element method (FEM) in an interior domain (port region) including moored ship region and an analytical approximation in the unbounded region (open sea) is utilized to determine the wave response of moored ship motion. Especially, in this approach, a FEM and analytical approximation are firstly utilized to solve MSE with the consideration of permeable breakwaters for moored ship motion under the resonance conditions. The non-uniform discretization pattern enhanced the numerical accuracy of the coupled numerical approach and is verified by using convergence analysis. Further, the simulation results are compared with existing studies to validate the applicability of the present numerical model. Wave absorbers and permeable breakwaters are employed to determine the incident wave response over moored ship motion inside the realistic Paradip port, Odisha, India. In addition, the efficacy of permeable breakwaters and wave absorbers on moored ship motion is investigated. It is shown that breakwaters and wave absorbers at appropriate locations play a significant role to induce/reduce the resonance inside the port. Therefore, the current numerical model provides the countermeasures tactics such as installing breakwaters, wave absorbers to mitigate the resonance in arbitrarily shaped ports for safe moorings.

Numerical Simulation of Wind Waves and calculation of planning wave factors in the East Taihu Lake, Jiangsu Province, China

Taihu Lake is a large shallow lake in the lower Yangtze River Delta. The wave action in Taihu Lake plays an important role in coastal port construction. In this paper, based on the 10 min average wind speed at 10 m above the water surface recorded hourly from August 14 to August 17, 2014, the SWAN wave model is used to simulate the wind waves of the Taihu Lake in the corresponding period. Due to the lack of long-time series of wave observation data in the project area, the relationship between design wind speed and wind wave is used to calculate wave elements in different return periods. The results show that the strong wind direction and strong wave direction of the East Taihu Lake are NNW. The waves in the proposed Qidu harbor are mainly from the waves outside the permeable breakwater. Under the action of the most unfavorable wave direction NE, the effective wave height of most waters in the harbor is below 0.4m, which can meet the requirements of avoiding waves for fishing boats.

Bragg resonant reflection of water waves by a Bragg breakwater with porous trapezoidal bars on a sloping permeable seabed

For water waves propagating over a permeable sea bottom, a one-dimensional modified mild-slope equation (MMSE) is briefly derived considering the effects of porous media and capable of describing a rapidly varying topography. The thickness of the porous layer is assumed to be infinite to reduce the computational cost. The present numerical model has been validated against Rojanakamthorn et al.’s (1989) experiment for waves transformation over a submerged permeable breakwater on an impermeable seabed, Mase and Takeba's (1994) numerical solution for waves over a porous rippled bed and Liu et al.’s (2020) analytical solution for wave propagation over a series of submerged trapezoidal bars, respectively. A good agreement is obtained. More computational results show that the wave energy will be dissipated in the permeable bottom, and it will achieve the maximal values near the positions of Bragg resonant reflection. The peak Bragg resonance increases with an increasing number of bars and bar slope. However, it decreases with an increase in the permeability, bar submergence, and slope of the seabed. Moreover, there exists a particular value of the bar width that maximizes the Bragg resonant reflection.

Performance evaluation of submerged breakwater using Multi-Domain Boundary Element Method

The gravity wave interaction with submerged breakwater of different structural configurations are investigated based on the small-amplitude wave theory. The boundary value problem is analysed in two-dimension using the linearized wave theory in water of finite depth. The submerged breakwater structural configuration such as (i) thin-walled type (impermeable), (ii) rectangular type (impermeable and permeable), (iii) triangular type (impermeable, permeable, perforated), (iv) trapezoidal type (impermeable, permeable, perforated) and (v) Tandem type (impermeable, permeable, perforated) are considered to analyse and performance of the breakwater. The numerical model is developed using the Multi-Domain Boundary Element Method (MDBEM) to analyse the hydrodynamic scattering coefficient (such as reflection, transmission and dissipation coefficient) for the change of physical parameters such as relative spacing between the breakwaters, relative water depth and structural dimensions. The convergence of the present numerical model is performed for the specific case of tandem breakwater and numerical computation is validated with the results available in the literature. The wave reflection and transmission coefficient along with wave force on the structure is analysed for different shapes, structural parameters and geometrical parameters of the breakwater to maximize the efficiency of breakwater. In the case of permeable breakwater, the submerged tandem breakwater is found to be more efficient in wave transformation as compared to rectangular, triangular and trapezoidal permeable submerged breakwaters. The comparative analysis performed on different configurations of the breakwater in the present study will be helpful in the effective design of the breakwater near the harbour regions.

Coastal erosion on the north coast of Java: adaptation strategies and coastal management

Coastal erosion remains a problem for the socio-economic development of the coastal zone in the north coast of Java. This study aims to determine the coastal characteristics, shoreline changes, and adaptation strategies of the north coast of Java through satellite study and on-ground observations. The analysis covers two decadal periods of satellite data starting from 1998 to 2018. The coastal characteristic of the north coast of Java is typified by sandy, muddy, and gravelly coast. At particular coasts have been extensively modified becoming coastal structure buildings. The shoreline changes are characterized by sectors alternating between erosion and accretion, although in general indicating the erosion processses. The conversion of mangrove ecosystems into fish ponds along with an increase of coastal constructions such as groins, jetties, and seawalls may have strong influences on the coastal erosion at the particular coastal environments. Since traditional hard defense methods used so far have had more damaging than protective effects, there is a need now for the use of soft prevention alternatives and for providing new guidelines for coastal management. A set of permeable breakwater measures, in conjunction with sediment managing schemes, are proposed for the sustainable development of the coastal zone.

Fully Coupled Simulation of Interactions Among Waves, Permeable Breakwaters and Seabeds Based on N-S Equations

Interstitial flows in breakwater cores and seabeds are a key consideration in coastal and marine engineering designs and have a direct impact on their structural safety. In this paper, a unified fully coupled model for wave-permeable breakwater-porous seabed interactions is built based on an improved N-S equation. A numerical wave flume is constructed, and numerical studies are carried out by applying the finite difference method. In combination with a physical model test, the accuracy of the numerical simulation results is verified by comparing the calculated and measured values of wave height at measurement points and the seepage pressure within the breakwater and seabed. On this basis, the characteristics of the surrounding wave field and the internal flow field of the pore structure, as well as the evolution process of the fluctuating pore water pressure inside the breakwater and seabed, are further analyzed. The spatial distribution of the maximum fluctuating pore water pressure in the breakwater is compared between two cases by considering whether the seabed is permeable, and then the effect of seabed permeability on the dynamic pore water pressure in the breakwater is clarified. This study attempts to provide a reference for breakwater design and the protection of nearby seabeds.

Mathematical modeling of arbitrary shaped harbor with permeable and impermeable breakwaters using hybrid finite element method

A mathematical model is developed based on the application of permeable and impermeable breakwaters utilizing the mild slope equation (MSE) to analyze the wave amplification in an arbitrary shaped harbor with variable bathymetry. Finite element method (FEM) coupled with analytical approximation is described as Hybrid FEM, which is used to solve the MSE and Helmholtz equation in bounded and unbounded domains (open Sea region), respectively. The validation of the present numerical scheme is conducted by comparing the simulation results with the existing studies and the convergence analysis is also conducted to verify the accuracy of the numerical scheme. The effects of energy dissipation, bottom friction, and variable wave transmission through impermeable and permeable breakwaters are investigated to understand the resonance phenomenon in rectangular port. In addition, the current numerical scheme is implemented on a real Paradip port, Odisha, India at six different key locations, and for the first time the effect of breakwaters placed at the entrance and in the bounded region, along with bottom friction, and partially reflecting port boundary are investigated. The breakwaters with small permeability/transmission coefficient have high efficiency to reduce the wave resonance inside the port.

ANALISIS REFLEKSI DAN TRANSMISI GELOMBANG PADA PEMECAH GELOMBANG TIANG PANCANG

Pantai berlumpur rentan terhadap kerusakan akibat gelombang, sehingga diperlukan perlindungan pantai yang salah satunya menggunakan pemecah gelombang tipe permeable. Tipe permeable yang dikembangkan ini disebut sebagai Pemecah Gelombang Tiang Pancang. Bahan yang digunakan untuk memodelkan struktur tersebut (prototipe) di laboratorium adalah bambu bulat bersekat yaitu bambu bulat dari taman Pringgodani dengan diameter 1 cm, tinggi 20 cm dengan sekat kayu multiblok setebal 2 cm. Analisis refleksi dan transmisi terhadap hasil pengujian model fisik 2D terhadap pemecah gelombang diperlukan untuk mencapai optimasi dalam penggunaannya. Hasil pengujian laboratorium membuktikan bahwa Pemecah Gelombang ini cukup efektif pada skenario yang memiliki nilai Kt yang lebih kecil dan nilai Kr yang lebih besar. Pada percobaan ini pengujian dilakukan dengan skenario tinggi muka air pada Mean Sea Level (MSL) (44 cm) dan High Water Level (HWL) (50 cm) dengan 2 skenario spasi antar tiang yaitu 1 cm dan 2 cm pada masing-masing tinggi muka air. Kemudian hasil perhitungan Kt dan Kr dibandingkan dengan variabel non-dimensional kecuraman gelombang (Hi/gT2) dan kemiringan gelombang (Hi/L) . Hasil percobaan laboratorium menunjukkan bahwa nilai Kt lebih rendah pada saat kondisi MSL, dan nilai Kr lebih tinggi pada saat kondisi MSL hal ini menunjukkan bahwa Pemecah Gelombang Bambu Bulat Bersekat ini lebih efektif pada muka air rendah dari pada muka air tinggi.

A Study on Minimization of Harbor Oscillations by Infragravity Waves Using Permeable Breakwater

A Study on Minimization of Harbor Oscillations by Infragravity Waves Using Permeable Breakwater

A CASE STUDY ON HARBOR OSCILLATIONS BY INFRAGRAVITY WAVES

In this study, the minimization of harbor oscillation using permeable breakwater was applied to the actual harbor and investigated a reduction effect by computer simulation in order to take into account the water quality problems and measures of harbor oscillation by infragravity waves at the same time. The study site is Mukho harbor located at east coast of Korea. The infragravity waves which obtained by analyzing the field data for five years focused on the distribution between wave periods of 40s and 70s and wave heights in less than 0.1m was 94percent of analyzing data. The target wave periods for minimization of harbor oscillation was 68s. The most effective method of minimization of harbor oscillation by infragravity waves was to install a detached permeable breakwater with transmission coefficient of 0.3 on the outside harbor and replace some area of the vertical wall with wave energy dissipating structure to achieve a reflectivity of 0.9 or less in a harbor. The reduction rate of amplitude shown in 27.4percent in this method.Recorded Presentation from the vICCE (YouTube Link): https://youtu.be/oDzrehaXlY8

Permeable Breakwaters Performance Modeling: A Comparative Study of Machine Learning Techniques

The advantage of permeable breakwaters over more traditional types has attracted great interest in the behavior of these structures in the field of engineering. The main objective of this study is to apply 19 well-known machine learning regressors to derive the best model of innovative breakwater hydrodynamic behavior with reflection and transmission coefficients as the target parameters. A database of 360 laboratory tests on the low-scale breakwater is used to establish the model. The proposed models link the reflection and transmission coefficients to seven dimensionless parameters, including relative chamber width, relative rockfill height, relative chamber width in terms of wavelength, wave steepness, wave number multiplied by water depth, and relative wave height in terms of rockfill height. For the validation of the models, the cross-validation method was used for all models except the multilayer perceptron neural network (MLP) and genetic programming (GP) models. To validate the MLP and GP, the database is divided into three categories: training, validation, and testing. Furthermore, two explicit functional relationships are developed by utilizing the GP for each target. The exponential Gaussian process regression (GPR) model in predicting the reflection coefficient (R2 = 0.95, OBJ function = 0.0273), and similarly, the exponential GPR model in predicting the transmission coefficient (R2 = 0.98, OBJ function = 0.0267) showed the best performance and the highest correlation with the actual records and can further be used as a reference for engineers in practical work. Also, the sensitivity analysis of the proposed models determined that the relative height parameter of the rockfill material has the greatest contribution to the introduced breakwater behavior.

Wave and Hydrodynamic Processes in the Vicinity of a Rubble-Mound, Permeable, Zero-Freeboard Breakwater

A numerical study for the effect of crest width, breaking parameter, and trunk permeability on hydrodynamics and flow behavior in the vicinity of rubble-mound, permeable, zero-freeboard breakwaters (ZFBs) is presented. The modified two-dimensional Navier-Stokes equations for two-phase flows in porous media with a Smagorinsky model for the subgrid scale stresses were solved numerically. An immersed-boundary/level-set method was used. The numerical model was validated for the cases of wave propagation over a submerged impermeable trapezoidal bar and a low-crested permeable breakwater. Five cases of breakwaters were examined, and the main results are: (a) The size of the crest width, B, does not notably affect the wave reflection, vorticity, and currents in the seaward region of ZFBs, while wave transmission, currents in the leeward side, and mean overtopping discharge all decrease with increasing B. A non-monotonic behavior of the wave setup is also observed. (b) As the breaking parameter decreases, wave reflection, transmission, currents, mean overtopping discharge, and wave setup decrease. This observation is also verified by relevant empirical formulas. (c) As the ZFB trunk permeability decreases, an increase of the wave reflection, currents, wave setup, and a decrease of wave transmission and mean overtopping discharge is observed.

2D water-wave interaction with permeable and impermeable slopes: Dimensional analysis and experimental overview

The main objective of this research is to characterize and quantify the prevalent physical processes in the energy transformation of a regular wave train when it interacts with permeable and impermeable breakwaters. Two sources of experimental data are considered: (a) numerical experiments on an undefined impermeable rigid slope, using the numerical model (IH–2VOF), and (b) physical experiments on a non-overtoppable permeable breakwater with a cube armor layer and a porous core of finite width in a 2D wave flume. A revised dimensional analysis reveals that the relative water depth, h/L, and the incident wave steepness, H/L, at the toe of permeable and impermeable breakwaters are the key factors to define and optimize the experimental space (HI/L, h/L). Moreover, the product of (h/L) (HI/L) can be applied to identify the type of wave breaking and the domains of wave energy transformation, and to quantify the reflected and transmitted energy coefficients and the dissipation rate (KR2,KT2,D∗). Fitting an experimental curve (i.e. a sigmoid function) to the impermeable data, the slope is a plotting parameter. The same conclusion is obtained for a permeable breakwater; in addition the wave energy coefficients depend on the relative breakwater width B*/L, and the relative core grain size and D50,p/L, and armor unit diameter, Da/L. Because the range of the design factors spans several orders of magnitude, a log-transformation provides a well behaved experimental space [ln(h/L), ln(H/L)] which is likely of benefit to verify the wave breaker type and the related dissipation-reflection-transmission on slopes. Finally, this study shows that there is not a biunivocal relationship between the Iribarren number, Ir, and the type of breaker, the reflection and transmission coefficients and the bulk dissipation. Therefore, Iribarren's number is not a sufficient similarity parameter for the analysis of wave breaking, and related flow characteristics on slopes.

A Framework for Plans Permeable Breakwater Eco-Friendly Building Identification and Characteristics Materials Construction Study Case at Demak Village

A Framework for Plans Permeable Breakwater Eco-Friendly Building Identification and Characteristics Materials Construction Study Case at Demak Village

Seismic dynamic response analysis of permeable breakwater on piled foundation considering pile-soil interaction

In order to discuss the seismic response of pile foundation permeable breakwater structure under different working conditions, the dynamic implicit module in finite element software ABAQUS is used to analyze the seismic dynamic response of pile foundation permeable breakwater. Considering the nonlinear characteristics of pile-soil interaction the breakwater is simulated under different seismic intensity conditions. The acceleration, bending moment of pile foundation are analyzed by time-history analysis method. The influence of pile diameter on the whole structure is compared. The results show that the stronger the earthquake is, the more obvious the overall dynamic response of the structure is. The bending moment of pile body decreases first and then increases. The wider the diameter of pile foundation, the greater the stiffness of the whole structure, resulting in an increase in the seismic force received by the structure. Compared with the static load, the influence of earthquake on the permeable pile breakwater can not be ignored.

An Extensive Analysis of Oscillations in Arbitrary Harbors with Reflecting, Absorbing and Transmitting Boundaries – Case study of the Port of Indiana

The harbor resonance numerical model can be applied to wave response in the harbor, groups of linear and nonlinear waves with high crest pose hazards to ships, inducing harbor resonance and over-topping of structures. The model, a two-dimensional linear, inviscid, dispersive, hybrid finite element to simulate harbor resonance with conservation of energy approach, is applicable in an offshore or coastal harbor of arbitrary shape. The model incorporates the effects of variable bathymetry, bottom friction, variable, full or partial absorbing boundaries as well as wave transmission through permeable breakwaters. The accuracy and efficiency of the present model will be verified by comparing with those of experimental and field data of the Port of Indiana, where wave incidences of ship damage, broken mooring lines and barge sinking, particularly in the grain dock area. It is important to study the behavior of incident wave periods and the associated maximum harbor resonant response at key points within the harbor. The model results were proved to be consistent with observations which lead to the conclusion that the model is well suited for use in harbors of irregular geometry with transmissivity boundaries. The model presented herein is a realistic method for solving arbitrary harbor resonance problems.

A model for obliquely incident wave interacting with a multi-layered object

This paper presents an analytical solution for scattering of oblique incident, small amplitude, monochromatic wave trains by a stationary rigid multi-layered objects with rectangular cross-section. The object is infinite long and consists of multilayers, which can be either solid or permeable. This paper extends the previous work by Hu and Liu [1] from normal incident wave condition with a special object configuration to oblique incident waves with multi-layered object. The present model is validated with several existing solutions for normal/oblique waves interacting with a single object; excellent agreement is observed. New numerical results are presented to investigate the effects of incidence angle on reflection, transmission and energy loss coefficients for a combined floating and bottom-mounted permeable breakwater. A new floating board-cage breakwater is developed from the present model and its solutions are discussed in detail. A computer program, AWAS-P, has been updated so that it is applicable for both oblique and normal incident waves, while the object is multi-layered.

Meshless Method for Analysis of Permeable Breakwaters in the Proximity of A Vertical Wall

In the present work, the improved version of the meshless singular boundary method (ISBM) is developed for analyzing the performance of bottom standing submerged permeable breakwaters in regular normally incident waves and in the proximity of a vertical wall. Both single and dual prismatic breakwaters of rectangular and trapezoidal forms are examined. The physical problem is cast in terms of the Laplace equation governing an irrotational flow and incompressible fluid motion with appropriate mixed type boundary conditions, and solved numerically using the ISBM. To model the permeability of the breakwaters fully absorbing boundary conditions are assumed. Numerical results are presented in terms of hydrodynamic quantities of the reflection coefficients. These are firstly validated against the results of a multi-domain boundary element method (BEM) developed independently for a previous study. The agreement between the results of the two methods is excellent. The coefficients of reflection are then computed and discussed for a variety of structural conditions including the breakwaters height, width, spacing, and absorbing permeability. Effects of the proximity of the vertical plane wall are also investigated. The breakwater’s width is found to have only marginal effects compared with its height. Permeability tends to decrease the minimum reflections. These coefficients show periodic variations with the spacing relative to the wavelength. Trapezoidal breakwaters are found to be more cost-effective than the rectangular breakwaters. Dual breakwater systems are confirmed to perform much better than single structures.

Asymptotic Expansion and Numerical Solution for Gravity Waves in a Porous Media

In this paper, we study wave interaction with a porous structure. A nonlinear diffusive wave equation is used to describe gravity surface wave propagation in a porous media. We solve the equations using asymptotic expansion method and numerically using a staggered finite volume method. We then derive the dispersion relation that holds for gravity waves inside a porous structure. This dispersion relation explains the diffusive mechanism of wave amplitude inside the porous structure. Analysis of the dispersion relation shows that amplitude reduction depends on porous medium parameters such as porosity, friction coefficient, length of the structure, and wave frequency. To validate our numerical scheme, we compare the wave reduction amplitude from the numerical result with the asymptotic solution. A good agreement of the comparison is observed. Furthermore, the numerical model is employed to investigate the effectiveness of porous media in dissipating wave energy of an incoming wave. The results from this paper can be used to determine the optimum dimension of the porous medium so that the incoming wave can be reduced as much as possible to protect shoreline. References H.J.S. Fernando, S.P. Samarawickrama, S. Balasubramanian, S.S.L. Hettiarachchi, and S. Voropayev. Effects of porous barriers such as coral reefs on coastal wave propagation. Journal of Hydro-environment Research, 1(3):187 – 194, 2008. Pengzhi Lin and S. A. Karunarathna. Numerical study of solitary wave interaction with porous breakwaters. Journal of Waterway, Port, Coastal, and Ocean Engineering, 133(5):352–363, 2007. Philip L.-F. Liu, Pengzhi Lin, Kuang-An Chang, and Tsutomu Sakakiyama. Numerical modeling of wave interaction with porous structures. Journal of Waterway, Port, Coastal, and Ocean Engineering, 125(6):322–330, 1999. Patrick J. Lynett, Philip L.-F. Liu, Inigo J. Losada, and Cesar Vidal. Solitary wave interaction with porous breakwaters. Journal of Waterway, Port, Coastal, and Ocean Engineering, 126(6):314–322, 2000. O.S. Madsen. Wave transmission through porous structures. Journal of Waterways, Harbors, Coastal Engineering, 100:169–188, 1974. I. Magdalena, S. R. Pudjaprasetya, and L. H. Wiryanto. Wave interaction with an emerged porous media. Advances in Applied Mathematics and Mechanics, 6(5):680–692, 06 2015. S.R. Pudjaprasetya and I. Magdalena. Momentum conservative scheme for dam break and wave run up simulations. East Asia Journal on Applied Mathematics, 4(2):152–165, 2014. Panagiotis D. Scarlatos and Vijay P. Singh. Long-wave transmission through porous breakwaters. Coastal Engineering, 11(2):141 – 157, 1987. C.K. Sollitt and R.H. Cross. Long-wave transmission through porous breakwaters. Proc. 13th Coastal Eng. Conf. 3, pages 1827–1846, 1972. W. Sulisz. Wave reflection and transmission at permeable breakwaters of arbitrary cross-section. Coastal Engineering, 9:371–386, 1985. M. R. A. Van Gent. Wave interaction with permeable coastal structures. International Journal of Rock Mechanics and Mining Sciences and Geomechanics Abstracts, 33(6):277A, 1996.