Porosity effects on non-breaking surface waves over permeable submerged breakwaters

This study investigated how the porosity of submerged breakwaters affects non-breaking wave transformations. Eight model geometries each with six different porosities, from 0.421 to 0.912, were also considered. Experimental results reveal that the model width has little effect on wave reflection and transmission when the model heights are fixed. The transmission coefficient is maximum at a kh in the range from 1.3 to 2.0 and minimum at a kh around 0.7. The wave reflection maximum is at kh of near 0.5. The energy loss of the primary waves is maximum near kh=0.81 and minimum when the porosity of the model is large. Porosity does affect wave transformation and its influence becomes significant as the heights of the models increase. For the range of porosities tested, wave energy loss from the primary harmonic was found to be almost constant at around 0.4 when kh >1.3, decreasing slowly when kh <1.3; wave energy loss decreases for porosities above 0.75.     

Random wave-induced onshore scour characteristics around submerged breakwaters using a stochastic method

This paper provides a stochastic method by which the two-dimensional onshore scour characteristics along the base of submerged breakwaters exposed to normally incident random waves on both sloping and horizontal sandy seabed can be derived. Here the formulas for the regular wave-induced scour characteristics provided by Young and Testik (2009) are used. These formulas are combined with describing the waves as a stationary Gaussian narrow-band random process to derive the random wave-induced onshore scour characteristics; the maximum scour depth, the scour length, and the distance of the maximum scour depth location from the onshore breakwater face. An example of calculation is also provided.     

Experimental study of strong reflection of regular water waves over submerged breakwaters in tandem

A series of laboratory experiments was carried out to investigate the strong reflection of regular water waves over a train of submerged breakwaters. Rectangular and trapezoidal shapes of submerged breakwaters are employed and compared for reflecting capability of incident waves. Measured reflection coefficients of regular waves over impermeable submerged breakwaters are verified by comparing with those of the eigenfunction expansion method. A very good agreement is observed. Reflection coefficients of permeable submerged breakwaters are less than those of impermeable breakwaters. The trapezoidal shape is recommended for a submerged breakwater in terms of reflecting capability and practical application.     

Wave motion over a submerged breakwater with an upper horizontal porous plate and a lower horizontal solid plate

This study examines the hydrodynamic performance of a modified two-layer horizontal-plate breakwater. The breakwater consists of an upper submerged horizontal porous plate and a lower submerged horizontal solid plate. By means of the matched eigenfunction expansion method, a linear analytical solution is developed for the interaction of water waves with the structure. Then the reflection coefficient, the transmission coefficient, the energy-loss coefficient and the wave forces acting on the plates are calculated. The numerical results obtained for limiting cases are exactly the same as previous predictions for a single submerged horizontal solid plate and a single submerged horizontal porous plate. Numerical results show that with a suitable geometrical porosity of the upper plate, the uplift wave forces on both plates can be controlled at a low level. Numerical results also show that the transmission coefficient will be always small if the dimensionless plate length (plate length versus incident wavelength) exceeds a certain moderate value. This is rather significant for practical engineering, as the incident wavelength varies over a wide range in practice. Moreover, it is found that the hydrodynamic performance of the present structure may be further enhanced if the lower plate is also perforated.     

淹没矩形防波堤透反射系数特性研究

采用解析方法研究了斜向入射波作用下淹没矩形防波堤的透反射系数特性.首先利用特征函数展开法导出了绕射势函数的分析解和透反射系数的计算公式,然后利用边界元方法验证了解析解,在此基础上利用解析解分析了若干工况下的防波堤透反射特性.计算结果表明,淹没矩形防波堤截面的宽度、高度和相对位置以及入射角的改变都不同程度影响反射系数和透射系数.在中等深度条件下,对于一定频率的波浪,位置和尺寸适当的淹没矩形堤可以反射大部分斜向入射波.研究结果对设计淹没的矩形防波堤具有重要的参考价值.     

Scattering of water wave by a submerged horizontal plate and a submerged permeable breakwater

Based on a two-dimensional linear water wave theory, this study develops the boundary element method (BEM) to examine normally incident wave scattering by a fixed, submerged, horizontal, impermeable plate and a submerged permeable breakwater in water of finite depth. Numerical results for the transmission coefficients are also presented. In addition, the numerical technique's accuracy is demonstrated by comparing the numerical results with previously published numerical and experimental ones. According to that comparison, the transmission coefficient relies not only on the submergence of the horizontal impermeable plate and the height of the permeable breakwater, but also on the distance between horizontal plate and permeable breakwater. Results presented herein confirm that the transmission coefficient is minimum for the distance approximately equal to four times the water depth.     

Numerical study for waves propagating over a porous seabed around a submerged permeable breakwater: PORO-WSSI II model

The phenomenon of the wave, seabed and structure interactions has attracted great attentions from coastal geotechnical engineers in recent years. Most previous investigations have based on individual approaches, which focused on either flow region or seabed domain. In this study, an integrated model (PORO-WSSI II), based on the Volume-Averaged/Reynolds-Averaged Navier-Stokes (VARANS) equations and Biot's poro-elastic theory, is developed to investigate the mechanism of the wave-permeable structure-porous seabed interactions. The new model is verified with the previous experimental data. Based on the present model, parametric studies have been carried out to investigate the influences of wave, soil and structure parameters on the wave-induced pore pressure. Numerical results indicated: (i) longer wave period and larger wave height will obviously induce a higher magnitude of pore pressure at the leading edge of a breakwater; (ii) after a full wave-structure interaction, the magnitude of pore pressure below the lee side of a breakwater decreases with an increasing structure porosity while it varies dramatically with a change of structure height; and (iii) the seabed thickness, soil permeability and the degree of saturation can also significantly affect the dynamic soil behaviour.     

The interaction of surface water waves with submerged breakwaters

This paper concerns the behaviour of nonlinear regular waves interacting with rectangular submerged breakwaters. A new series of experimental results is presented and compared with numerical calculations based upon a Boundary Element Method (BEM) that utilises multiple fluxes to deal with the discontinuities encountered at the corners of the domain. Specifically, comparisons concern both the spatial water surface profiles at various times and the spatial evolution of the harmonics generated by the breakwaters, the latter being an important focus for the paper. The BEM is shown to accurately model both the water surface profile and the harmonic generation, provided the breakwater width is sufficient to ensure that flow separation is not a controlling influence. Furthermore, evidence is provided to confirm that reflection from rectangular submerged breakwaters is fundamentally a linear phenomenon.     

Bragg reflection of sinusoidal waves due to trapezoidal submerged breakwaters

Numerical and laboratory experiments are performed to investigate characteristics of the Bragg reflection due to multi-arrayed trapezoidal submerged breakwaters. The numerical model is based on the Reynolds averaged Navier–Stokes equations with the VOF method and the k–ε turbulence closure model. As expected, the reflection coefficients increase as the array of submerged breakwaters increases in both laboratory measurements and numerical results. The resonant periods provide similar relative wave numbers regardless of the permeability and the number of arrays. The reflection coefficients due to porous breakwaters are smaller than those due to non-porous breakwaters. The velocity contours for two and three arrays are also described.     

Experimental study on the performance of the multiple-layer breakwater

Based on the idea of disturbing the water motion in the upright direction, a new kind of multiple-layer breakwater is proposed in this article, which mainly consists of several horizontal plates. The breakwater's performance of dissipating waves has been investigated in detail in the regular wave tests. The factors identified with the characteristics of the breakwater are discussed, such as the relative width, the wave steepness and the models geometrical parameters (the width and the gap). The comparison and analysis of the transmission and reflection coefficients with respect to different factors are presented. The model test results indicate that the multiple-layer breakwater has the good characteristic of dissipating waves. Further more, only in a little extent can it reflect the waves. The multiple-layer breakwater proposed in the paper is very significative to promote the open type breakwater to be the permanent wave attenuator in the application.     

削角直立式防波堤可靠度分析

根据最新导出的荷载变量相关时结构可靠指标β的Hasofer-Lind计算方法，利用特定地点的长期波浪观测资料，对明、暗基床的削角直立式防波堤进行了可靠度分析，得出了可靠指标β与传统设计方法中安全系数K的关系曲线，进而给出了削角直立堤抗滑移和抗倾覆极限状态下各项分项系数的建议值。     

Deformation of rubble-mound breakwaters under cyclic loads

Rubble-mound breakwaters usually consist of a core of small quarry-run rock protected by one or more intermediate layers or underlayers that separate the core from the cover layers, which are composed of large armor units. Failure of rubble-mound breakwaters may be due to effects such as removal or damage of the armor units, overtopping leading to scouring, toe erosion, loss of the core material, or foundation problems under waves. However, whether rubble mounds fail under seismic loads is unknown. High seismic activity can lead to large settlements and even to failure of the breakwaters. The design of coastal structures should take into account the most relevant factors in each case, including seismic loading. The objective of this study is to understanding the failure mechanisms of conventional breakwater structures under seismic loads on rigid foundations. Hence, an experimental study was carried out on conventional breakwater structures with and without toes, subjected to different dynamic loadings of variable frequencies and amplitudes, in a shaking tank. A shaking tank with a single degree of freedom was developed to study the simple responses of conventional rubble-mound breakwaters under cyclic loads. For each test, an automatic raining crane system was used to achieve the same relative density and porosity of the core material. The input motion induced horizontal accelerations of different magnitudes during the tests. The accelerations and the deformation phases of the model were measured by a data acquisition system and an image processing system. The experiments on the conventional rubble-mound type breakwater model were performed under rigid-bottom conditions. The model's scale was 1:50. Cyclic responses of breakwaters with toes and without toes were examined separately, and their behaviors were compared. The results were compared with a numerical study, and the material properties and failure modes were thus defined.     

部分反射直墙前潜堤水动力特性研究

基于线性势流理论,对部分反射直墙前潜堤的水动力特性进行了理论研究。利用匹配特征函数展开法给出了潜堤透射系数和反射系数的计算方法,计算结果与边界元方法的计算结果一致。利用数值算例分析了潜堤透射系数和反射系数的主要影响因素。增大部分反射直墙的反射系数,将加大潜堤的透射系数。随着潜堤相对宽度或潜堤与直墙之间相对间距的增加,潜堤透射系数和反射系数呈周期性变化,但变化规律相反。     

透空式防波堤周围的非线性波浪传播的数值模拟

对非线形波浪在透空式防波堤周围的波浪变形进行了数值模拟,在Boussinesq波浪方程中加入与透空建筑物有关的新的耗散项,从而界定了透空建筑物引起的部分反射和透射,波浪折射衍射的传播过程通过控制方程求解。波浪控制方程通过有限差分方法求解。模型应用于模拟波浪经过具有部分反射的群桩式透空结构,结果表明透空式防波堤可以有效地衰减波浪,是重力式结构的一种替代形式。     

Geometrical properties of perfect breaking waves on composite breakwaters

The experimental results have so far shown that when a wave breaks on a vertical wall with an almost vertical front face at the instant of impact that is called perfect breaking or perfect impact, the greatest impact forces are produced on the wall. Therefore, the configuration of breaking waves is important in the design considerations of coastal structures. The present study is concerned with determining the geometrical properties of oscillatory waves that break perfectly on the vertical wall of composite-type breakwaters. The laboratory tests for perfect breaking waves on composite breakwaters are conducted with base slopes of 1/2, 1/4 and 1/6, and with berm widths of 0.00, 0.10, 0.20, 0.30 and 0.40 m. The shape and the dimensions of waves at the instant of perfect breaking on the wall are determined using a video camera. The experimental results for the geometrical properties of the breakers are presented non-dimensionally. Within the range of present experimental conditions, it is found that the dimensionless breaker crest height, h_b/d_w, and dimensionless breaker height, H_b/d_w, decrease; and, dimensionless breaker depth, d_w/H₀, increases with increasing relative berm width, B/D. The breaker height index, H_b/H₀, is almost unaffected by B/D. The deep-water wave steepness and the base slope of the breakwater do not seem to influence the geometrical properties of the breakers at wall systematically.     

Numerical analysis of wave overtopping of rubble mound breakwaters

The paper describes the results of a two-dimensional (2-D) numerical modelling investigation of the functionality of rubble mound breakwaters with special attention focused on wave overtopping processes. The model, COBRAS-UC, is a new version of the COBRAS (Cornell Breaking Waves and Structures) based on the Volume Averaged Reynolds Average Navier–Stokes (VARANS) equations and uses a Volume of Fluid Technique (VOF) method to capture the free surface. The nature of the model equations and solving technique provides a means to simulate wave reflection, run-up, wave breaking on the slope, transmission through rubble mounds, overtopping and agitation at the protected side due to the combined effect of wave transmission and overtopping. Also, two-dimensional experimental studies are carried out to investigate the performance of the model. The computations of the free surface and pressure time series and spectra under regular and irregular waves, are compared with the experimental data reaching a very good agreement. The model is also used to reproduce instantaneous and average wave overtopping discharge. Comparisons with existing semi-empirical formulae and experimental data show a very good performance. The present model is expected to become in the near future an excellent tool for practical applications.     

Hydrodynamic performance of a dual cylindrical caisson breakwater

The hydrodynamic performance of a dual cylindrical caisson breakwater (DCBW) formed by a row of caissons each of which consisting of a porous outer cylinder circumscribing an impermeable inner cylinder has been theoretically investigated. The theoretical formulation is based on the eigenfunction expansion method proposed by Spring and Monkmeyer (1974) which was further modified by Linton and Evans [Linton, C.M., Evans, D.V., 1990. The interaction of waves with arrays of vertical circular cylinders. Journal of Fluid Mechanics 215, 549–569] for an array of impermeable cylinders. The present formulation is an extension of the work of Wang and Ren [Wang, K.H., Ren, X., 1994. Wave interaction with a concentric porous cylinder system. Ocean Engineering 21(4), 343–360], wherein; the interaction of linear waves with a single concentric porous cylinder system was studied. In the present study, the formulation has been extended to the case of a group of porous dual cylinder system. Parametric studies are carried out to study the influence of porosity (G₀) on the outer caisson, width of the doughnut chamber (a/b) and the angle of wave incidence on the variation in the hydrodynamic loading, wave run-up, free-surface elevation in its vicinity as well as the transmission on its lee-side. The importance of the presence of the inner cylinder in achieving the required hydrodynamic performance in terms of either protection or providing tranquility on its lee side keeping higher stability for the breakwater system is highlighted.     

多向聚焦波作用下透水潜堤消波特性数值模拟研究

本文采用非静压模型NHWAVE建立高精度三维波浪数值水槽,对多向聚焦波作用下透水和不透水潜堤消波特性进行数值模拟研究。通过计算结果与实验数据的对比,验证了该模型模拟多向聚焦波产生传播及多孔介质内流动的能力,进一步考虑了有效波高、水深、谱峰周期和传播角度等因素对潜堤消波特性的影响。结果表明：潜堤对多向聚焦波的最大波幅、最大水位、沿水深平均最大流速和波能均有显著消减作用,且透水潜堤因孔隙介质的存在消波性能更好。随着有效波高增大,堤顶处波浪破碎点前移,不透水潜堤消波性能受波高影响较大。水深越大,潜堤消波性能越低。透水潜堤对长周期波浪消减效果较差。传播角度越小,聚焦位置处波幅越大,波浪非线性作用越强。研究结果可为我们进一步保护沿海设施免受极端海洋环境的影响提供一定的参考