Simplified analytical solutions for wave interaction with absorbing-type caisson breakwaters

Simplified analytical solutions are presented to model the interaction of linear waves with absorbing-type caisson breakwaters, which possess one, or two, perforated or slotted front faces which result in one, or two, interior fluid regions (chambers). The perforated/slotted surfaces are idealized as thin porous plates. Energy dissipation in the interior fluid region(s) inside the breakwater is modelled through a damping function. Under the assumption of potential flow and linear wave theory a boundary-value problem may then be formulated to describe wave interaction with the idealized structure. A solution to this simplified problem may be obtained by an eigenfunction expansion technique and an explicit analytical expression may be obtained for the reflected wave height. Using the experimental work of previous authors, damping coefficients are determined for both single and double chamber absorbing-type caisson breakwaters. Based on the damping for a single perforated-wall breakwater, a methodology is proposed to enable the estimation of the damping coefficients for a breakwater with two chambers. The theoretical predictions of the reflection coefficients for the two-chamber structures using the present model are compared with those obtained from laboratory experiments by other authors. It is found that the inclusion of the damping in the interior fluid region gives rise to improved agreement between theory and experiment.     

Investigation of Π-type breakwaters performance under regular and irregular waves

In this paper, performance of solid and perforated Π-type breakwaters was investigated experimentally. Both regular and irregular waves were used during testing. Four depths of immersions were selected for each breakwater and wave type. Different wave groups were generated over these breakwaters, and the transmission, reflection and energy-dissipation characteristics were determined. The results of the experimental study were evaluated and some empirical expressions based on the results were suggested to define the transmission, reflection and energy-dissipation coefficients for different immersion depths of solid and perforated breakwaters under regular and irregular waves. Moreover, performance of solid and perforated Π-type breakwaters were compared with that of solid and perforated U-type breakwaters investigated by Günaydın and Kabdaşlı [2006. Performance of solid and perforated U-type breakwaters under regular and irregular waves. Ocean Engineering 31, 1377–1405]. These comparisons showed that the most reasonable model and wave type are selected to determine requiring performance parameters.     

Performance of solid and perforated U-type breakwaters under regular and irregular waves

An experimental investigation of U-type breakwaters was carried out in a laboratory channel. Both regular and irregular waves were used during testing. Two types of breakwaters such as solid and perforated were studied to analyse the porosity effect of structures. In order to investigate performance of these breakwaters for different immersion depths, four depths of immersions of the solid and perforated breakwaters were selected. Different wave groups were generated over these breakwaters, and the transmission, reflection and energy dissipation characteristics of each breakwater were determined. Three coefficients such as transmission, reflection and energy dissipation coefficients, which were named as C_t, C_r, and C_l, respectively, were used during the evaluation of the test results. The most important parameters governing performance of these breakwaters were determined by using earlier investigations and experimental results. These parameters were expressed as a dimensionless group by using π theory. Based on the test results, empirical expressions were formulated to describe the C_t, C_r, and C_l for different immersion depths of solid and perforated breakwaters under regular and irregular waves.     

Analytical and Experimental Studies on Hydrodynamic Performance of Semi-Immersed Jarlan-Type Perforated Breakwaters

The present study proposes a new semi-immersed Jarlan-type perforated breakwater including a perforated front wall, a solid rear wall, and a horizontal perforated plate connecting the lower tips of the two walls. An analytical solution is developed to estimate the hydrodynamic performance of the new breakwater. The analytical solution is confirmed by solutions for special cases, an independently developed multi-domain boundary element method solution and experimental data. Numerical examples based on the analytical solution indicate that compared with previous semi-immersed breakwaters, the new breakwater may have better wave-absorbing performance and smaller wave forces. Some useful results are presented for practical designs of semi-immersed Jarlan-type perforated breakwaters.     

Wave Scattering by Double Slotted Barriers in A Steady Current： Experiments

The adoption of slotted breakwaters can be an ideal option in the protection of very large near-shore floating struc-trees that may extend offshore to a considerable water depth. In this paper, we experimently investigated the behaviour of wave transmission and reflection coefficients of double slotted barriers in the presence of a steady opposing current. The experimental results show that opposing currents have only minor effects on wave reflection, but can significantly reduce the wave transmission through double slotted barriers. The experimental results suggest that coastal currents should be taken into consideration for an economical design of slotted breakwaters.     

Wave interaction with one or two rows of closely spaced rectangular cylinders

Experimental results are reported on the wave reflection from and transmission through one row or two rows of closely spaced rectangular cylinders. An empirical expression is proposed for the friction factor which models the head loss due to closely spaced rectangular cylinders. Algebraic expressions are presented to calculate the reflection and transmission coefficients of regular waves for a single slotted wall or double slotted walls. The model is validated by the published and present experimental results. The proposed method can be used for the preliminary design of slotted-wall breakwaters.     

Wave interactions with multiple-row curtainwall-pile breakwaters

In this study, a mathematical model has been developed that can compute various hydrodynamic characteristics of a multiple-row curtainwall-pile breakwater. To examine the validity of the developed model, laboratory experiments have been conducted for double- and triple-row breakwaters with various combinations of drafts of curtain walls, porosities between piles, and distances between rows. Comparisons between measurement and prediction show that the mathematical model adequately reproduces most of the important features of the experimental results. As a whole, the transmission coefficient decreases with an increase in relative water depth, whereas the reflection coefficient, normalized run-up and force exhibit an opposite trend in their variations. With fixed values of the draft of the curtain wall and the porosity of lower perforated part of the first row of a double-row breakwater, as these values of the second row increase and decrease, respectively, the transmission coefficient decreases, as expected. On the other hand, their effects on wave reflection, run-up, and wave force change with the relative depth. As for the distance between the rows, the transmission coefficient becomes a maximum when it is about one half of the wave length, suggesting that this condition should be avoided to achieve the advantage of the breakwater in reducing wave transmission. It is shown that for prototype breakwaters, on an average, the transmission coefficient would be smaller than 0.3 for wave periods less than 6.0 s, and it would be about 0.45 even for the wave period of 9.0 s, although there would be a variation depending on the geometry of the breakwater. It is also shown that wave transmission is significantly reduced by multiple-row breakwaters compared with a single-row breakwater, while the difference between double-row and triple-row breakwaters is marginal. Finally, engineering monograms are provided for double-row breakwaters to be used in practical engineering applications of the breakwaters.     

Hydrodynamic modeling of perforated structures

A hydrodynamic model of perforated or slotted structures is proposed. It is asymptotic in the sense that the openings are supposed to be infinitely small and numerous, and the wall thickness to be nil. At variance with other work, a quadratic, not linear, law, relating the pressure differential to the traversing velocity, is assumed. As a result the hydrodynamic coefficients (added mass and damping) become amplitude dependent. The model is applied to bodies of various shapes including cylinders, plates and disks, in forced motion or submitted to incoming waves. Good agreement with experimental data is generally observed.     

多层挡板桩基透空式防波堤消浪特性试验研究

本文回顾了已有的关于透空式防波堤的波浪透射率的理论计算方法,分析了多层挡板桩基透空式防波堤的消浪机理。结合防波堤断面波浪试验,探讨多层挡板桩基透空式防波堤的消浪特性。研究结果表明多层挡板桩基透空式防波堤能够显著消减波浪,它的应用突破了透空式防波堤仅适用于小尺度风浪水域的经验。研究发现影响防波堤消浪效果的因素中,挡板的透空率和设置方式的影响最为显著。文中提出的减小波浪透射率的方法可供设计部门参考。     

多消浪室局部开孔沉箱防波堤反射特性的迭代解析研究

基于势流理论,对多消浪室局部开孔沉箱防波堤的反射特性进行解析研究。研究中采用开孔墙处的二次压力损失边界条件,可以直接考虑波高对于开孔墙处能量损失的影响。利用匹配特征函数展开法和迭代方法得到当前问题的解析解。收敛性验证表明,迭代计算和级数解均具有良好的收敛性。该解析解的计算结果与分区边界元的数值计算结果一致,并且与已有的试验结果符合良好。通过算例分析,研究开孔沉箱防波堤反射系数的主要影响因素。结果表明：与单消浪室开孔沉箱防波堤相比,多消浪室开孔沉箱防波堤可以在更宽的波浪频率范围内保持低反射;增大开孔墙的开孔率,有利于降低多消浪室开孔沉箱防波堤的反射系数;当开孔墙的开孔率沿着入射波方向依次递减时,多消浪室开孔沉箱防波堤的反射系数较小。本文所建立的解析模型简单可靠,可用于工程初步设计中分析开孔沉箱防波堤的水动力性能。     

Brief Account of Breakwater Construction in China

-The construction of breakwaters in China in more than 40 years since the founding of the People's Republic of China is reviewed. The construction of two main types of breakwater, upright breakwaters and rubble mound breakwaters, and the way in which they are built are expounded. Recommendations to improve the technology for future breakwater construction are presented.     

Analytical Research on Wave Diffraction on Arc-Shaped Bottom-Mounted Perforated Breakwaters

An analytical method is developed to study wave diffraction on arc-shaped and bottom-mounted perforated breakwaters.The breakwater is assumed to be rigid,thin,vertical,immovable and located in water of constant depth.The fluid domain is divided into two regions by imaginary interface.The velocity potential in each region is expanded by eigenfunctions.By satisfying the continuity of pressure and normal velocity across the imaginary fluid interface,a set of linear algebraic equations can be obtained to determine the unknown coefficients of eigenfunctions.Numerical results,in the form of contour maps of the relative wave amplitude around the breakwater,are presented for a range of wave and breakwater parameters.Results show that the wave diffraction on the arc-shaped and bottom-mounted perforated breakwater is related to the incident wavelength and the porosity of the breakwater.The porosity of the perforated breakwater may have great effect on the diffracted field.     

Numerical Simulation of Wave Interaction with Perforated Caisson Breakwaters

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Calculation of Wave Pressure and Pressure Spectrum for Perforate-Pipe Breakwater

Standing waves are formed due to the reflection when waves meet vertical wall,thereforestrong structures are needed to keep the wall stability under the serious wave attack.For the improvementof the working condition and increase of the stability of the wall,the lower reflecting breakwaters have at-tracted close attention Reports mostly from Japanese researchers are often concerned with the wall ofcaisson equipped with open windows.In this paper a kind of hollow-pipe perforated breakwater is exam-ined which waves may partially perforate into the harbour basin.The wave in front of the wall can onlyform partial standing wave and wave force is reduced obviously.And the theoretical calculation of waveforce and analysis of wave force spectrum are all derived.Comparison between the results from theoreticalcalculation and hydraulic modeling shows reasonable agreement.     

Placement Effect on the Stability of Tetrapod Armor Unit on Breakwaters in Irregular Waves

Tetrapod, one of the well-known artificial concrete units, is frequently used as an armor unit on breakwaters. Two layers of tetrapod units are normmaly placed on the breakwaters with different placement methods. In this study, the stability of tetrapod units with two different regularly placement methods are investigated experimentally in irregular waves. Stability coefficients of tetrapod units for both placement methods are obtained. The important characteristic wave parameters of irregular waves causing the same damage ratio as those of the regular waves are also determined. It reveals that the average of one-tenth highest wave heights within the wave train (H_1/10) causes the similar damage as regular waves.     

Deformation of breakwater armoured artificial units under cyclic loading

Rubble mound breakwaters usually consist of armour, filter and core layers. The units used in the armour layer are natural rock or concrete. Although natural rock is usually preferred, it is not always possible to apply it. There are some advantages to using concrete units: they have a high stability coefficient under wave attack, and they are easily produced at work sites. Tetrapod and cube blocks are widely used in breakwaters as armour units.Rubble mound breakwaters are subjected not only to wave activity but also other types of environmental loading, such as earthquakes. Although rubble-mound breakwaters are most likely the most common type of breakwaters, they have received little attention regarding their response to seismic activity. The objective of this study is to present the dynamic response of a breakwater armoured by tetrapods placed by two different placement methods and armoured by cubes during seismic loadings experimentally and numerically. A shaking tank was developed for the experimental study. The breakwater models sit on a rigid bed, and the model scale is 1/50. A one-dimensional shaking tank was used to understand simple responses of the rubble mound breakwaters under seismic loads. The tank allows only one degree of freedom. A raining crane system was developed to achieve the same packing density and porosity for the core material. The shape of the model breakwater before and after the tests was measured using a profiler and was recorded by computer. However, crest lowering and the level of damage on slopes were determined from profiler records. The dynamic responses of the model breakwaters were also investigated using an image processing technique. For numerical simulation, software using finite element method was used.The results obtained from the experiment and numerical model may help designers build breakwaters armoured by artificial units.     

An experimental study of wave scattering by a vertical slotted barrier in the presence of a current

In coastal waters, tidal currents and surface waves co-exist. In this study, the influence of a steady current on the scattering of waves by a vertical slotted barrier is investigated experimentally in a wave flume. The separation of the incident and reflected waves is carried out by a two-point method that takes into account the effects of the current. Results show that currents significantly increase the wave-energy loss by the barrier and remarkably reduce the wave transmission through the barrier. It is suggested that the tidal currents should be taken into consideration in an economical design of slotted breakwaters.     

The new wave overtopping database for coastal structures

Significant effort has been made to generate a homogeneous database on wave overtopping consisting of more than 10,000 irregular wave overtopping tests from more than 160 independent projects or test series, each described by means of 31 parameters. Many coastal structures, including dikes, rubble mound breakwaters, berm breakwaters, caisson structures and combinations have been considered and have been schematised for inclusion in the database. All these overtopping tests are represented by over 300,000 numbers in the database.     

波浪作用下堤前冲淤研究综述

总结了近年来国内外对波浪作用下堤前冲淤的研究状况,包括规则波和不规则波作用下堤前海床的冲淤形态、冲淤形态判别标准、冲淤机理等.针对该课题的研究现状,提出了需进一步研究的问题.     

A new formula for front slope recession of berm breakwaters

The front slope stability of breakwaters with a homogeneous berm was studied in a large number of two dimensional model tests at Aalborg University, Denmark. The results are presented together with a new formula for prediction of the berm recession which is the most important parameter for describing the reshaping. The formula has also been calibrated and validated against model test data from other researchers. The significance of the new design formula is that it predicts berm recession much better than the existing methods, especially in case of more stable structures.