Random wave-induced scour at the trunk section of a breakwater

This paper provides a stochastic method by which the random wave-induced scour depth at the trunk section of vertical-wall and rubble-mound breakwaters can be derived. Here the formulas for regular wave-induced scour depth provided by Xie [Xie, S.L., 1981. Scouring patterns in front of vertical breakwaters and their influence on the stability of the foundations of the breakwaters. Report. Department of Civil Engineering, Delft University of Technology, Delft, The Netherlands, September, 61 pp.] for vertical-wall breakwater and Sumer and Fredsøe [Sumer, B.M., Fredsøe, J., 2000. Experimental study of 2D scour and its protection at a rubble-mound breakwater. Coast. Eng. 40, 59–87] for rubble-mound breakwater are used. These formulas are combined with describing the waves as a stationary Gaussian narrow-band random process to derive the random wave-induced scour depth. Comparisons are made between the present method and the Sumer and Fredsøe [Sumer, B.M., Fredsøe, J., 2000. Experimental study of 2D scour and its protection at a rubble-mound breakwater. Coast. Eng. 40, 59–87.] random wave scour data for rubble-mound breakwater, as well as the Hughes and Fowler [Hughes, S.A., Fowler, J.A., 1991. Wave-induced scour predictions at vertical walls. ASCE Proc. Conf. Coastal Sediments vol. 91, 1886–1899] random wave scour data and formula for vertical-wall breakwater. A tentative approach to random wave-induced scour at a vertical impermeable submerged breakwater is also suggested.     

2-D numerical analysis of near-field flow at low-crested permeable breakwaters

This paper describes the capability of a numerical model named COrnell BReaking waves And Structures (COBRAS) [Lin, P., Liu, P.L.-F., 1998. A numerical study of breaking waves in the surf zone. Journal of Fluid Mechanics 359, 239–264; Liu, P.L.-F., Lin, P., Chang, K.A., Sakakiyama, T., 1999. Numerical modeling of wave interaction with porous structures. Journal of Waterway, Port, Coastal and Ocean Engineering 125, 322–330, Liu, P.L.-F., Lin, P., Hsu, T., Chang, K., Losada, I.J., Vidal, C., Sakakiyama, T., 2000. A Reynolds averaged Navier–Stokes equation model for nonlinear water wave and structure interactions. Proc. Coastal Structures '99, 169–174] based on the Reynolds Averaged Navier–Stokes (RANS) equations to simulate the most relevant hydrodynamic near-field processes that take place in the interaction between waves and low-crested breakwaters. The model considers wave reflection, transmission, overtopping and breaking due to transient nonlinear waves including turbulence in the fluid domain and in the permeable regions for any kind of geometry and number of layers. Small-scale laboratory tests were conducted in order to validate the model, with different wave conditions and breakwater configurations. In the present study, regular waves of different heights and periods impinging on a wide-crested structure are considered. Three different water depths were tested in order to examine the influence of the structure freeboard. The experimental set-up includes a flow recirculation system aimed at preventing water piling-up at the lee of the breakwater due to overtopping. The applicability and validity of the model are examined by comparing the results of the numerical computations with experimental data. The model is proved to simulate with a high degree of agreement all the studied magnitudes, free surface displacement, pressure inside the porous structure and velocity field. The results obtained show that this model represents a substantial improvement in the numerical modelling of low-crested structures (LCS) since it includes many processes neglected previously by existing models. The information provided by the model can be useful to analyse structure functionality, structure stability, scour and many other hydrodynamic processes of interest.     

Numerical analysis of wave loads for coastal structure stability

The numerical model COBRAS-UC [Losada, I.J., Lara, J.L., Guanche,R., Gonzalez-Ondina, J.M. (2008). Numerical analysis of wave overtopping of rubble mound breakwaters. Coastal Engineering, Vol 55 (1), 47–62.] is used to carry out a two-dimensional analysis of wave induced loads on coastal structures. The model calculates pressure, forces and moments for two different cross-sections corresponding to a low-mound and a conventional rubble-mound breakwater with a crown-wall under regular and irregular incident wave conditions. Predicted results are compared with experimental information provided in Losada et al. [Losada, I.J., Lara, J.L., Guanche,R., Gonzalez-Ondina, J.M. (2008). Numerical analysis of wave overtopping of rubble mound breakwaters. Coastal Engineering, Vol 55 (1), 47–62.] and Lara et al. [Lara, J.L., Losada, I.J., Guanche, R. (2008). “Wave interaction with low mound breakwaters using a RANS model”. Ocean engineering (35), pp 1388–1400; doi:10.1016/j.oceaneng.2008.05.006.] on a 1:20 scale. Good agreement is found, and the differences between both typologies are explained in detail. Additionally, numerical results are also compared with several semi-empirical formulae recommended for design at both the 1:20 model scale and two prototype cross-sections. Results suggest that COBRAS-UC is able to provide realistic stability information that can be used to complete the approach based on currently existing methods and tools.     

波浪与抛石潜堤相互作用的MPS法数值模型研究

为了研究波浪与抛石潜堤相互作用过程中大自由表面变形和堤内渗流等强非线性紊流运动问题,利用改进的MPS法,建立了模拟波浪与抛石潜堤相互作用的MPS法数值计算模型。模型将抛石潜堤假定为均质多孔介质,采用Drew的二相流运动方程描述多孔介质内外的流体运动;通过在动量方程中增加非线性阻力项,并引入亚粒子尺度紊流模型,模拟波浪与可渗结构物相互作用过程中的紊流运动。选取“U”型管中多孔介质内渗流过程和孤立波与可渗潜堤相互作用两个典型的渗流问题,通过将数值计算结果与理论解和实测值的对比分析,对所提出的MPS法紊流渗流模型的模拟精度进行验证。结果表明:基于改进的MPS法构建的垂向二维紊流渗流模型可以很好地再现“U”型管中多孔介质内渗流以及波浪作用下可渗潜堤内外的复杂流场,显著缓解流-固界面处的压力震荡与粒子分布不均匀问题,实现了较高的模拟精度。     

半潮堤前的反射形态与时均流速场分析

采用模型试验和数值模拟研究了不同水深工况下半潮堤前的反射形态及时均流速场。基于Hilbert变换建立了叠合波的时频分离技术,同时获取了入射波和反射波的波面过程及相位关系,通过试验数据证明其适用于不同反射程度的波浪信号分析。不同水深工况下,半潮堤前形成了部分立波系统,腹点和节点分别以四分之一波长的偶数倍和奇数倍交替增加。半潮堤前底床水质点水平速度包络图与波面包络图相差四分之一周期的相位,水平速度的极大值和极小值分别出现在波面包络图的节点和腹点,意味着节点处易形成冲刷,腹点处易形成淤积。3种工况的周期平均速度场均在迎浪基床上方的堤脚处存在一个小型环流系统,可能引起局部冲刷,此处需加强防护。淹没工况下,半潮堤前的周期平均速度场形成一个大型环流系统,表层水流向堤后,中下层水流向海侧,意味着底床悬起的泥沙很可能向离岸方向流失。     

深水工况下弧面胸墙沉箱堤的反射形态分析

为推广应用新型弧面胸墙沉箱堤,结合模型试验和数值模拟对比分析了深水工况下弧面胸墙沉箱堤和削角胸墙沉箱堤的反射形态。波面和波压的数值结果与试验数据吻合良好,验证了数值方法的有效性。反射系数表明,入射波浪在与弧面胸墙沉箱堤相互作用过程中的能量损耗最小,其反射强于削角胸墙沉箱堤。波面和流速包络图显示,两种堤型均在堤前形成了部分立波系统,腹点和节点以四分之一波长的距离增量交替出现,胸墙和直立部分产生的反射波存在相位差,导致初始腹点的位置向海侧偏移。弧面胸墙沉箱堤前叠合波的相位差影响最小,腹点包络高度最大,节点包络高度最小,反射效应最明显。两种堤型前中下层水流的周期平均速度均较小且对称,表明底床泥沙不会产生趋势性输移,但迎浪基床上方的环流系统可能引起局部冲刷。相对而言,弧面胸墙沉箱堤前的环流强度最弱,更有利于冲刷防护。     

聚焦波浪在浅堤上传播变形高精度数值模拟研究

基于开源程序REEF3D,通过建立高精度二维数值波浪水槽,系统研究了聚焦波浪在浅堤上传播变形的规律,着重分析了聚焦波浪通过浅堤的水动力过程及能量变化规律,讨论了不同波浪要素对聚焦波浪传播特性的影响。除此之外,还考虑了双浅堤布置对聚焦波浪传播变形的影响。研究结果表明:极端波浪通过浅堤时,堤顶水深越小,波浪主频能量衰减越显著。在给定堤顶水深条件下,聚焦点与浅堤的相对位置对聚焦波浪能量的衰减影响较小。在双浅堤布置条件下,随着浅堤间距的增加,上下游浅堤的相互影响逐渐减弱,高频段的波浪能量也随之减小。     

The role of submerged berms on the momentary liquefaction around conventional rubble mound breakwaters

Berms deployed at the toe of conventional rubble mound breakwaters can be very effective in improving the stability of the armor layer. Indeed, their design is commonly tackled by paying attention to armor elements dimensioning. Past research studies showed how submerged berms can increase the stability of the armor layer if compared to straight sloped conventional breakwaters without a berm. To fill the gap of knowledge related to the interaction between breakwaters with submerged berm, waves and soil, this research aims to evaluate how submerged berms configuration influences the seabed soil response and momentary liquefaction occurrences around and beneath breakwaters foundation, under dynamic wave loading. The effects of submerged berms on the incident waves transformation have been evaluated by means of a phase resolving numerical model for simulating non-hydrostatic, free-surface, rotational flows. The soil response to wave-induced seabed pressures has been evaluated by using an ad-hoc anisotropic poro-elastic soil solver. Once the evaluation of the seabed consolidation state due to the presence of the breakwater has been performed, the dynamic interaction among water waves, soil and structure has been analyzed by using a one-way coupling boundary condition. A parametric study has been carried out by varying the berm configuration (i.e. its height and its length), keeping constant the offshore regular wave condition, the berm and armor layer porosity values, the water depth and the elastic properties of the soil. Results indicate that the presence of submerged berms tends to mitigate the liquefaction probability if compared to straight sloped conventional breakwater without a berm. In addition, it appears that the momentary liquefaction phenomena are more influenced by changing the berm length rather than the berm height.     

港域波浪数学模型的改进与验证

通过物理模型对改进的港内波浪传播变形数学模型进行验证。该数学模型以推广的时变缓坡方程为控制方程,采用含松弛因子的ADI法求解,并对波浪反射和透射边界模拟方法进行改进。先通过物理模型试验确定斜向浪入射条件下抛石防波堤前的波浪反射系数,作为数学模型中部分反射边界模拟的依据。然后进行了一个典型港口内波浪折射、绕射和反射的模型试验,测量港内波浪分布。对比模型试验和数学模型计算的结果表明,数学模型可较好地模拟港内复杂地形和边界条件下规则波和不规则波的传播变形。     

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.     

Verification of A Numerical Harbour Wave Model

A numerical model for wave propagation in a harbour is verified by use of physical models.The extended time-dependent mild slope equation is employed as the governing equation,and the model is solved by use of ADI method containing the relaxation factor.Firstly,the reflection coefficient of waves in front of rubble-mound breakwaters under oblique incident waves is determined through physical model tests,and it is regarded as the basis for simulating partial reflection boundaries of the numerical model.Then model tests on refraction,diffraction and reflection of waves in a harbour are performed to measure wave height distribution.Comparative results between physical and numerical model tests show that the present numerical model can satisfactorily simulate the propagation of regular and irregular waves in a harbour with complex topography and boundary conditions.     

Behaviour of rubble-mound breakwater in directional and uni-directional waves

The application of directional waves in design processes has clearly received much interest during recent years. Thus, in model testing with moored ships and offshore structures, significant deviations have been revealed between results obtained in traditional uni-directional wave trains and those obtained in directional wave fields. Whether the same tendency is valid in connection with the design of rubble mound breakwaters is studied in the present project. A breakwater with a front slope of 1:2 is tested at the scale 1:40. The weight and diameter of the stones in the core, filter and armour layers were carefully selected, and the sources of scatter in repeated tests were minimized. Furthermore, the incident wave energy was accurately adjusted to keep the same level in both uni-directional and directional waves. For the actual rubble-mound breakwater unambiguous results were obtained. When uni-directional waves were applied, the damage increased by 30–50% relative to the directional wave situation.     

柔性水囊潜堤消波特性的溃坝水槽试验研究

柔性水囊潜堤由橡胶制成，内部充水，具有结构简单、造价低廉等优点，能较好满足人工岛、跨海桥梁、海洋平台等基础设施建设工程对简单便携、拆装方便的临时防波堤的需求。为了探究柔性水囊潜堤的消波特性，在溃坝水槽内开展溃坝波与半圆柱形柔性水囊潜堤相互作用的试验研究，重点探究柔性水囊潜堤与溃坝波相互作用过程中水位变化特性，并与半圆柱刚性潜堤的性能进行比较；同时分析柔性水囊潜堤内部初始水压和浸没深度等参数对其消波性能的影响。结果表明：柔性水囊潜堤能够用作临时防波堤来衰减波浪；与半圆柱刚性潜堤相比，柔性水囊潜堤在降低溃坝波无量纲最大水位、提高消波性能方面更具优势；内部初始水压是影响柔性水囊潜堤消波性能的重要因素，适当降低内部初始水压，有利于增强柔性潜堤的变形程度，进而增加波能耗散，可获得更好的消波效果；而增加浸没深度即潜深，会使得柔性水囊潜堤对溃坝波的影响程度降低，消波效果减弱。     

Hydrodynamic characteristics of semi-immersed breakwater with an attached porous plate

In the present study, wave interaction with a fixed, partially immersed breakwater of box type with a plate attached (impermeable-permeable) at the front part of the structure is investigated numerically and experimentally. The large scale laboratory experiments on the interaction of regular waves with the special breakwater were conducted in the wave flume of Laboratori d’Enginyeria Marνtima (LIM) at Universitat Politecnica de Catalunya (UPC) in Barcelona. Experimental results are compared with numerical results obtained with the use of the Cornell breaking Wave and Structures (COBRAS) wave model. The effects of an impermeable as well as a permeable plate attached to the bottom of the breakwater on its hydrodynamic characteristics (wave transmission, reflection, dissipation, velocity and turbulence kinetic energy) are investigated. Computed velocities and turbulence kinetic energy in the vicinity of the structure indicate the effects of the breakwater with the attached (impermeable/permeable) plate on the flow pattern and the turbulence structure. The attached impermeable plate at the front part of the breakwater enhances significantly the efficiency of the structure in attenuating the incident waves. The permeable plate reduces the efficiency of the structure since wave energy is transmitted through the porous body of the plate. Based on the hydrodynamic characteristics it is inferred that the breakwater with an impermeable plate attached to its bottom is more efficient. The comparison of horizontal and vertical forces acting on the breakwater for all cases examined reveals that plate porosity influences slightly vertical force and severely horizontal force acting on the structure, reducing maximum values in both cases.     

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.     

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.     

Transmission of obliquely incident waves at low-crested breakwaters: Theoretical interpretations of experimental observations

The paper presents a series of analytical and numerical investigations of oblique wave transmission at low-crested breakwaters. For a smooth breakwater, two important features of wave height and direction are analyzed to establish the generic nature of the wave transmission process at oblique incidence. The proposed framework of research is validated against laboratory data from the EU-sponsored project, DELOS. The numerical simulations exhibit a significant decrease of the transmission coefficient with increasingly oblique incidence at a smooth breakwater. The roles of wave-breaking, nonlinearity, wave-induced currents and set-up in determining the characteristics of oblique wave transmission are demonstrated in the paper. It is found that both the amplitude-dependent phase velocity and the decrease of mean wave period contribute to the change of mean wave direction on the transmission side. An attempt has also been made to qualitatively explain the different behaviour of oblique wave transmission at a rubble-mound breakwater.     

Deformation of multi-directional random waves passing over an impermeable submerged breakwater installed on a sloping bed

This study investigates the wave deformation of multi-directional random waves passing over an impermeable submerged breakwater installed on the slope. Experiments were conducted in a three-dimensional wave basin equipped with a multi-directional random wave generator. Measurements of the free surface elevations around an impermeable submerged breakwater were carried out using 19 capacitance-type wave gages. In addition, a numerical model is proposed in three-dimensional random wave field. It is shown that the numerical results reproduce the general trend of the experimental results well. Investigations are made to study the effect of the spreading parameter S_max and bottom topography (bottom slope and submerged breakwater) on the wave deformation. It is pointed out that concentration of wave energy with larger values of the spreading parameter S_max is located within narrow limits in onshore side of the submerged breakwater. Furthermore, the supplementary discussion is made by means of numerical results.     

聚焦波作用下透水潜堤消波特性数值模拟研究

基于非静压数值计算模型,本文系统研究了聚焦波作用下透水潜堤的消波特性,通过设置合理的计算工况,详细分析了波高、堤顶水深、谱峰周期、孔隙率以及堤顶宽度5种因素对透水潜堤消波特性的影响。与此同时,本文将透水潜堤的计算结果同不透水潜堤的计算结果进行了对比分析。计算结果表明:透水潜堤对聚焦波的消减作用要强于不透水潜堤,从而说明,透水潜堤能更有效地降低畸形波对海岸基础设施的影响;波高和堤顶水深是影响潜堤消波特性的重要因素,随入射波高增加、堤顶水深减小,透水潜堤对波浪的消减作用逐渐增强。透水潜堤对长周期波浪的消波效果较差。在本文考虑的孔隙率范围内,孔隙率越大,透水潜堤消波效果越好;当孔隙率为0.4,堤顶宽度为0.612 5 m时,透水潜堤可消减54%的入射波能,比不透水潜堤对入射波能的消减增加36.1%。本文研究结果可为进一步认识透水潜堤的消波特性和海岸防护工程设计提供相应的参考。