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.     

近破波作用下沉箱式防波堤运动特性的模型实验研究

对近破波作用下沉箱式防波堤的运动特性进行了模型实验研究。实验中测量了沉箱模型与基床的摩擦系数、基床刚度和阻尼系数;不同水位情况下作用于沉箱模型上的近破波波压力时程;近破波作用下沉箱模型的位移和转角响应时程等,并与数学模型计算结果进行了比较分析。实验结果表明,若沉箱的滑移力大于沉箱与基床间的摩擦力,在连续波浪作用下,沉箱将连续出现间歇式滑移运动,数学模型可较好地模拟这一运动过程。     

单层开缝板沉箱防波堤水动力学特性研究

用阻抗分析方法,对有一块开缝板和一个消浪室组成的开缝板沉箱防波堤的波浪反射系数进行系统的研究。在对开缝板消波机理分析基础上,导出一个所有参数都可计算的、完全封闭的波浪反射系数理论公式。该式物理概念明确、结构简单,与已知学者的试验成果对比,理论与试验吻合良好。     

Dual floating breakwaters

A numerical model is developed to investigate the behavior of a pair of flexible, floating breakwaters consisting of complaint, beam-like structures anchored to the sea bed. Each structure is kept under tension by a small buoyancy chamber at the tip, additional stiffness in each case is provided by mooring lines attached to the buoyancy chamber. The fluid motion is idealized as linearized, two-dimensional potential flow and the equation of motion of each breakwater is taken to be that of a one-dimensional beam of uniform flexural rigidity and mass per unit length subjected to a constant axial force. The boundary integral equation method is applied to the fluid domain. Modifications are made to the basic formulation to account for the zero thickness of the idealized structures, and the dynamic behavior of the breakwaters is described through an appropriate Green's function. Numerical results are presented which illustrate the effects of the various wave and structural parameters on the efficiency of the two-breakwater systems as a barrier to wave action. It is found that by adjusting the spacing between the breakwaters acceptable wave reflection characteristics may be obtained even with relatively flexible structures.     

Floating pontoon breakwaters

The hydrodynamic properties of a pair of long floating pontoon breakwaters of rectangular section are investigated theoretically. The structures are partially restrained by linear symmetric moorings fore and aft. The fluid motion is idealized as linearized, two-dimensional potential flow. The breakwater motions are assumed to be two-dimensional, in surge, heave and pitch. The solution for the fluid motion is obtained by the boundary integral equation method using an appropriate Green's function. Numerical results are presented that illustrate the effects of the various wave and structural parameters on the efficiency of the breakwaters as barriers to wave action. It is found that the wave reflection properties of the structures depend strongly on their width, draft and spacing and the mooring line stiffnesses, while their excess buoyancy is of lesser importance.     

Hydrodynamic behavior of a straight floating pipe under wave conditions

This paper examines the hydrodynamic behavior of a floating straight pipe under wave conditions. The main problem in calculating the forces acting on a small-sized floating structure is obtaining the correct force coefficients C_n and C_t, which differ from a submerged structure. For a floating straight pipe of small size, we simplify it into a 2D problem, where the pipe is set symmetrically under wave conditions. The force equations were deduced under wave conditions and a specific method proposed to resolve the wave forces acting on a straight floating pipe. Results of the numerical method were compared to those from model tests and the effects of C_n and C_t on numerical results studied. Suggestions for the selection of correct C_n and C_t values in calculating wave forces on a straight floating pipe are given. The results are valuable for research into the hydrodynamic behavior of the gravity cage system.     

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。     

Wave interaction with T-type breakwaters

The wave transmission, reflection and energy dissipation characteristics of partially submerged ‘T'-type breakwaters (Fig. 1) were studied using physical models. Regular and random waves, with wide ranges of wave heights and periods and a constant water depth were used. Five different depths of immersions of the ‘T'-type breakwater were selected. The coefficient of transmission, K_t, coefficient reflection, K_r, were obtained from the measurements and the coefficient of energy loss, K_l is calculated using the law of conservation of energy. It is found that the coefficient of transmission generally reduces with increased wave steepness and increased relative water depth, d/L. This breakwater is found to be effective closer to deep-water conditions. K_t values less than 0.35 is obtained for both normal and high input wave energy levels, when the horizontal barrier of the T type breakwater is immersed to about 7% of the water depth. This breakwater is also found to be very efficient in dissipating the incident wave energy to an extent of about 65% (i.e. K_l>0.8), especially for high input wave energy levels. The wave climate in front of the breakwater is also measured and studied.

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Fig. 1. Schematic view of the T-type breakwater.     

Laboratory experiments on low-crested breakwaters

New unique laboratory experiments on low-crested structures (LCSs) have been performed within the DELOS project. The experiments were carried out in three European laboratories aiming at extending and completing existing available information with respect to a wide range of engineering design properties such as structural stability, wave and current flows and wave transmission. 3D wave basin tests were performed to provide information especially about the wave obliquity, where almost no research has been done before. Flow velocities inside and close to the surface of structures were studied in a wave channel at small scale, and scale effects regarding wave transmission and reflection were studied in a wave channel at a large scale facility. The paper describes the experiments and associated databank with respect to objectives, test program, set-ups and measurements. Results, guidelines and recommendations elaborated from the tests are included in the other companion papers of the Coastal Engineering Special Issue on DELOS.     

On rubble-mound breakwaters of composite slope

The geometrical properties of the armor layer of rubble mound breakwaters were investigated by observations made on two cases. The first case is a laboratory-scaled model of natural rock, designed with a composite slope. The second is a breakwater in the sea, constructed with a uniform slope of tetrapods. In both cases the cross-section underwent changes, resulting in an apparently stable profile of composite slope. This implied that for stability the optimal armour layer should be of composite slope. The general nature of this profile was implied by the geometrical similarity between the two cases which were basically so different.     

Long-wave transmission through porous breakwaters

An analytical model for the study of wave transmission through porous breakwaters is developed. The analysis is based on the principles of harmonic treatment of linearized long-wave equations. Wave motion within the porous structure is simulated both by Darcy and Dupuit-Forchheimer types of flow. The model includes the effects of damping due to bottom friction, and provides a more realistic presentation of the breakwater characteristics. A comparison with other existing theories and experimental data shows satisfactory agreement.     

Performance of pile-restrained flexible floating breakwaters

The overall performance of pile-restrained flexible floating breakwaters is investigated under the action of linear monochromatic incident waves in the frequency domain. The aforementioned floating breakwaters undergo only vertical structural deflections along their length and are held in place by means of vertical piles. The total number of degrees of freedom equals the six conventional body modes, when the breakwater moves as a rigid body, plus the extra bending modes. These bending modes are introduced to represent the structural deflections of the floating breakwater and are described by the Bernoulli–Euler flexible beam equation. The number of bending modes introduced is determined through an appropriate iterative procedure. The hydrostatic coefficients corresponding to the bending modes are also derived. The numerical analysis of the flexible floating breakwaters is based on a three-dimensional hydrodynamic formulation of the floating body. A parametric study is carried out for a wide range of structural stiffness parameters and wave headings, to investigate their effect on the performance of flexible floating breakwaters. Moreover, this performance is compared with that of the corresponding pile-restrained rigid floating breakwater. Results indicated that the degree of structural stiffness and the wave heading strongly affect the performance of flexible floating breakwaters. The existence of an “optimum” value of structural stiffness is demonstrated for the entire wave frequency range.     

Multidirectional wave transformation around detached breakwaters

The performance of the new wave diffraction feature of the shallow-water spectral model SWAN, particularly its ability to predict the multidirectional wave transformation around shore-parallel emerged breakwaters is examined using laboratory and field data. Comparison between model predictions and field measurements of directional spectra was used to identify the importance of various wave transformation processes in the evolution of the directional wave field. First, the model was evaluated against laboratory measurements of diffracted multidirectional waves around a breakwater shoulder. Excellent agreement between the model predictions and measurements was found for broad frequency and directional spectra. The performance of the model worsened with decreasing frequency and directional spread. Next, the performance of the model with regard to diffraction–refraction was assessed for directional wave spectra around detached breakwaters. Seven different field cases were considered: three wind–sea spectra with broad frequency and directional distributions, each coming from a different direction; two swell–sea bimodal spectra; and two swell spectra with narrow frequency and directional distributions. The new diffraction functionality in SWAN improved the prediction of wave heights around shore-parallel breakwaters. Processes such as beach reflection and wave transmission through breakwaters seem to have a significant role on transformation of swell waves behind the breakwaters. Bottom friction and wave–current interactions were less important, while the difference in frequency and directional distribution might be associated with seiching.     

Wave reflection from perforated-wall caisson breakwaters

Analytical models for predicting wave reflection from a perforated-wall caisson breakwater have been developed. Most of the existing models deal with the case in which the waves are normally incident to the caisson lying on a flat sea bottom. In the present paper, using the Galerkin-eigenfunction method, an analytical model is developed that can predict the reflection coefficient of a perforatedwall caisson mounted on a rubble mound foundation when waves are obliquely incident to the breakwater at an arbitrary angle. The developed model is compared with other theoretical results and hydraulic experimental data.     

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.     

Structural stability of detached low crested breakwaters

The aim of the paper is to describe hydraulic stability of rock-armoured low-crested structures on the basis of new experimental tests and prototype observations.Rock armour stability results from earlier model tests under non-depth-limited long-crested head-on waves are reviewed.Results from new 2-D and 3-D model tests, carried out at Aalborg University, are presented. The tests were performed on detached low-crested breakwaters exposed to short-crested head-on and oblique waves, including depth-limited conditions. A formula that corresponds to initiation of hydraulic damage and allows determining armour stone size in shallow water conditions is given together with a rule of thumb for the required stone size in depth-limited design waves.Rock toe stability is discussed on the basis of prototype experience, hard bottom 2-D tests in depth-limited waves and an existing hydraulic stability formula. Toe damage predicted by the formula is in agreement with experimental results. In field sites, damage at the toe induced by scour or by sinking is observed and the volume of the berm is often insufficient to avoid regressive erosion of the armour layer.Stone sinking and settlement in selected sites, for which detailed information is available, are presented and discussed.     

Rock toe stability of rubble mound breakwaters

The toe structure of a breakwater provides support to the armour layer and protects the structure from damage due to scour at the toe. Often a toe structure consists of rock material. Several design formulae exist to predict the amount of damage to the toe structure under wave loading. These design formulae for the required rock size include effects of the wave height and the water depth above the toe structure. Here, rock toe stability has been studied by means of physical model tests to provide information on the required rock size in the toe structure. The tests and analysis are focussed not only on the influence of the wave height and the water depth above the toe structure, but also on the influence of the width of the toe structure, the thickness of the toe and the wave steepness. The wave steepness, width of the toe and the thickness of the toe appear to affect the damage to the toe; these parameters need to be taken into account in order to derive accurate predictions of the damage to the toe structure. Based on the test results a prediction formula has been derived including these effects. The formula can be used to determine the required rock size in the toe of rubble mound breakwaters within the ranges of the performed tests.     

On front slope stability of berm breakwaters

The short communication presents application of the conventional Van der Meer stability formula for low-crested breakwaters for the prediction of front slope erosion of statically stable berm breakwaters with relatively high berms. The method is verified (Burcharth, 2008) by comparison with the reshaping of a large Norwegian breakwater exposed to the North Sea waves. As a motivation for applying the Van der Meer formula a discussion of design parameters related to berm breakwater stability formulae is given. Comparisons of front erosion predicted by the use of the Van der Meer formula with model test results including tests presented in Sigurdarson and Van der Meer (2011) are discussed. A proposal is presented for performance of new model tests with the purpose of developing more accurate formulae for the prediction of front slope erosion as a function of front slope, relative berm height, relative berm width, method of armour stone placement, and hydraulic parameters. The formulae should cover the structure range from statically stable berm breakwaters to conventional double layer armoured breakwaters.     

Numerical prediction of performance of submerged breakwaters

The results of a numerical model study on the transmission characteristics of a submerged breakwater are presented. Study aimed to determine the effect of depth of submergence, crest width, initial wave conditions and material properties on the transmission characteristics of the submerged breakwater. The results highlight the optimum crest width of the breakwater and optimum clear spacing between two breakwaters. A submerged permeable breakwater with d_s/d=0.5, p=0.3 and f=1.0, reduces the transmission coefficient by about 10% than the impermeable breakwater. The results indicates an optimum width ratio of B/d=0.75 for achieving minimum transmission. By restricting the effective width ratio of the series of breakwaters to 0.75, studies were conducted to determine the effect of clear spacing between breakwaters on transmission coefficient, suggesting an optimum clear spacing of w/b=2.00 to obtain K_t below 0.6.     

Long wave reflection from submerged trapezoidal breakwaters

This study addresses the reflection and transmission of long waves from a trapezoidal breakwater and a series of trapezoidal breakwaters, using the matching method. A systematic shape transfer is derived to determine wave reflection and transmission. The peak Bragg reflection of long waves from a series of trapezoidal breakwaters is shifted toward low frequency. In spite of the spacing between any pair of breakwaters, the top plane width and the arrangement of the series of breakwaters are found to be the two major parameters in designing multiply composite Bragg breakwaters.