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.     

Equilibrium scour depths around piles in noncohesive sediments under currents and waves

A universal formula for the estimation of equilibrium scour depth around a single cylindrical pile under the action of steady currents, tidal and short waves is presented.     

2D Wave setup behind submerged breakwaters

In addition to reducing the incoming wave energy, submerged breakwaters also cause a setup of the sea level in the protected area, which is relevant to the whole shadow zone circulation, including alongshore currents and seaward flows through the gaps. This study examines such a leading hydraulic parameter under the simplified hypothesis of 2D motion and presents a prediction model that has been validated by a wide ensemble of experimental data. Starting from an approach originally proposed by Dalrymple and Dean [(1971). Piling-up behind low and submerged permeable breakwaters. Discussion note on Diskin et al. (1970). Journal of Waterways and Harbors Division WW2, 423–427], the model splits the rise of the mean water level into two contributions: one is due to the momentum flux release forced by wave breaking on the structure, and the other is associated with the mass transport process. For the first time, the case of random wave trains has been explicitly considered.     

Modelling the effect of wave overtopping on nearshore hydrodynamics and morphodynamics around shore-parallel breakwaters

Wave overtopping nearshore coastal structures, such as shore-parallel breakwaters, can significantly alter the current circulation and sediment transport patterns around the structures, which in turn affects the formation of tombolos and salients in the nearshore area. This paper describes the implementation of a wave overtopping module into an existing depth-averaged coastal morphological mode: COAST2D and model applications to investigate the effect of wave overtopping on the hydrodynamics and morphodynamics around a group of shore-parallel breakwaters. The hydrodynamic aspects of the model were validated against a series of laboratory conditions. The model was then applied to a study site at Sea Palling, Norfolk, UK, where 9 shore-parallel segmented breakwaters including 4 surface-piercing and 5 low-crested breakwaters are present, for the storm conditions in Nov 2006. The model results were compared with laboratory data and field measurements, showing a good agreement on both hydrodynamics and morphological changes. Further analysis of wave overtopping effect on the nearshore hydrodynamics and morphodynamics reveals that wave overtopping has significant impacts on the nearshore circulation, sediment transport and the resulting morphological changes within such a complex breakwater scheme under the storm and macro-tide conditions. The results indicate the importance of including the wave overtopping in modelling nearshore morphodynamics with the presence of coastal structures.     

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.     

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.     

Performance of hemi-cylindrical and rectangular submerged breakwaters

A parametric experimental study is conducted to compare the reflection and transmission characteristics of submerged hemi-cylindrical and rectangular rigid and water-filled flexible breakwater models. The results show that, for the rigid breakwaters, rectangular models are more effective than hemi-cylindrical ones in terms of reduction of transmitted waves. As for the flexible breakwaters, the hemi-cylindrical models may give better wave reflection than rectangular ones. However, the energy loss induced by the rectangular breakwaters is much larger and more significant to result in an overall better efficiency in terms of reduction in wave transmission. The effects of internal pressure show that the lowest pressurized flexible models considered in this work are the most effective in the reduction of the transmitted wave height. Higher wave reflection, lower wave transmission and higher energy loss are obtained consistently at the lower submergence depth ratio.     

Current-induced scour around a vertical pile in cohesive soil

Stability of many ocean structures is affected by seabed scour induced by under-currents. The depth of scour is an important parameter for determining the minimum depth of foundations as it reduces the lateral capacity of the foundations. A review of the literature reveals that there is not much information available in the field of scour in cohesive soils. Hence, a detailed laboratory testing programme on model piles of diameters 50 mm to 110 mm embedded in soft silty clay soil was carried out in a wave flume of 30 m long, 2.0 m wide and 1.7 m deep, which has the capability of simulating steady currents. Scour around the pile due to steady streaming is monitored by using special instrumentation. A procedure has been suggested to predict the ultimate scour depths based on the observed variation in scour depth over a limited time period. The study indicates that the ultimate scour depth is controlled by diameter of obstruction, current velocity, model Reynolds number, flow Froude number, shear stress, and soil characteristics. Based on these results, a few functional relationships are suggested between scour depth and other parameters like Reynolds number, Froude number, and strength of the soil bed.     

A simplified instrumentation for measuring scour in silty clay around a vertical pile

The obstruction to flow around a pile placed in an erodible seabed causes scour leading to changes in the bed elevation in the vicinity of the pile. In the present investigation, scour around piles induced by the seabed current has been studied in a wave flume using model piles of diameters 50, 90 and 110 mm embedded in a silty clay soil bed. The particulate movement due to scour is time dependent and in case of sediments with particle sizes ranging upto clay fractions, the measurement of scour becomes extremely difficult. This paper presents a simplified experimental technique for the measurement of scour depth with time around a pile foundation in a silty clay soil.     

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.     

Dynamic pressures and forces exerted on impermeable and seaside perforated semicircular breakwaters due to regular waves

The semicircular breakwater (SBW) is a composite breakwater consisting of a semicircular caisson resting on a rubble mound. The SBW function as a barrier dissipates the incident wave energy and creates tranquillity on its leeside. The dynamic pressures due to regular waves exerted on seaside perforated SBWs with 7 and 11% of exposed surface area with perforations were measured. The measured pressures are compared with those exerted on impermeable SBWs. In addition, the forces exerted on the caisson alone are measured. The reflection coefficient, measured total forces on the caisson of the models, and the pressures are presented as functions of relative water depth. The effect of the water depth and the percentage of perforations on the above stated variables are examined, details of which are reported in this paper.     

Hydrodynamic studies on vertical seawall defenced by low-crested breakwater

This paper presents results obtained from a series of experiments conducted in wave flume to assess the influence of the offshore low-crested breakwater as a defence structure in reducing the wave forces on vertical seawall. The main aim of the tests was to know the effect of crest elevation of the offshore low-crested breakwater as a rehabilitation structure for the existing damaged shore protection structures. In this study five relative breakwater heights are used and associated flow evolution was analyzed. With the sections proposed in this study, it is possible to achieve considerable reduction of wave force on the seawall. Modification factor is proposed to estimate the shoreward force on the seawall defenced by low-crested breakwater.     

Wave reflection from vertical breakwater with porous structure

This paper presents numerical solutions for the wave reflection from submerged porous structures in front of the impermeable vertical breakwater. A new time-dependent mild-slope equation involves the parameters of the porous medium including the porosity, the friction factor and the inertia coefficient, etc. is derived for solving the boundary value problem. A comprehensive comparison between the present model and the existing analytical solution for the case of simple rectangular geometries of the submerged structure is performed first. Then, more complicated cases such as the inclined and trapezoidal submerged porous structures in front of the vertical breakwater with sloping bottom are considered. This study also examines the effects of the permeable properties and the geometric configurations of the porous structure to the wave reflection. It is found that the submerged porous structure with trapezoidal shape has more efficiency to reduce the wave reflection than that of triangular shape. The numerical results show that the minimum wave reflection is occurred when the breakwater is located at the intermediate water depth.     

Numerical study of the Reynolds-number dependence of two-dimensional scour beneath offshore pipelines in steady currents

A numerical model for local scour below pipelines is employed to investigate the Reynolds-number dependence of the two-dimensional scour beneath offshore pipelines in steady currents. A novel wall function is proposed in calculating the suspended sediment transport rate in the model. Scour developments beneath a model pipeline and the corresponding prototype pipeline are simulated under the same undisturbed Shields parameter but different values of Reynolds number. The effects of the Reynolds number difference on the scour profile development are investigated. It is found that scour depths for prototype pipelines are about 10–15% smaller than those for model pipelines. The flow phenomena that causes this difference are discussed by means of flow visualization. The normalized time scales are found to be approximately the same. The simulated scour profiles for the model pipelines agree well with the experimental results from an independent study.     

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.     

Numerical investigation on the dynamics of a vertical wall defenced by an offshore breakwater

The numerical and experimental investigations on the performance of an offshore-submerged breakwater in reducing the wave forces and wave run-up on vertical wall are presented. A two-dimensional finite-element model is employed to study the hydrodynamic performance of the submerged breakwater under the action of regular and random waves. The numerical prediction has been supported with experimental measurements. The wave forces and wave run-up on the vertical wall were measured for different breakwater configurations. The applicability of linear theoretical model in the prediction of wave forces on the wall by a submerged breakwater has been discussed.     

直立式防波堤口门区海啸局部冲刷规律实验研究

海啸作为世界上最严重的自然灾害之一,其巨大的破坏力使得近海建筑物遭受了严重的损害。基于波浪水槽实验,开展海啸波作用下不同口门距离的防波堤局部冲刷机理实验研究。实验结果表明,在海啸波越顶水流产生的水跌以及海啸波通过防波堤口门时产生的扰流共同作用下,口门中心线处产生明显的局部冲刷坑,随着口门距离的增加,防波堤局部冲刷先加剧后减弱。建立防波堤局部最大冲刷深度与海啸波波高、防波堤宽度及出水高度、口门间距的关系式,揭示了最大局部冲刷深度与海啸波波高、防波堤尺寸、口门距离的内在关系。     

Breaking wave loads at vertical seawalls and breakwaters

This paper presents recent advances in knowledge on wave loads, based on experimental work carried out in the CIEM/LIM large flume at Barcelona within the framework of the VOWS (Violent Overtopping by Waves at Seawalls) project. Both quasi-static and impact wave forces from the new data set have been compared with predictions by empirical and analytical methods. The scatter in impact forces has been found to be large over the whole range of measurements, with no existing method giving especially good predictions. Based on general considerations, a simple and intuitive set of prediction formulae has been introduced for quasi-static and impact forces, and overturning moments, giving good agreement with the new measurements. New prediction formulae have been compared with previous measurements from physical model tests at small and large scale, giving satisfactory results over a relatively wide range of test conditions. The time variation of wave impacts is discussed, together with pressure distribution up the wall, which shows that within experimental limitations the measured pressures are within existing limits of previous study.     

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.