Prediction of Seaward Slope Recession in Berm Breakwaters Using M5' Machine Learning Approach

In the design process of berm breakwaters, their front slope recession has an inevitable rule in large number of model tests, and this parameter being studied. This research draws its data from Moghim's and Shekari's experiment results. These experiments consist of two different 2D model tests in two wave flumes, in which the berm recession to different sea state and structural parameters have been studied. Irregular waves with a JONSWAP spectrum were used in both test series. A total of 412 test results were used to cover the impact of sea state conditions such as wave height, wave period, storm duration and water depth at the toe of the structure, and structural parameters such as berm elevation from still water level, berm width and stone diameter on berm recession parameters. In this paper, a new set of equations for berm recession is derived using the M5' model tree as a machine learning approach. A comparison is made between the estimations by the new formula and the formulae recently given by other researchers to show the preference of new M5' approach.     

An experimental study on the reshaping of berm breakwaters under irregular wave attacks

The main idea concerned with the design of berm breakwaters is to construct a less expensive structure with reshaping berm. An experimental study on the front slope stability of homogeneous berm breakwaters has been carried out in a large number of 2D model tests at Tarbiat Modares University. In this paper, the results of this experimental study are presented conjointly with a formula for estimation of berm recession as the most important parameter for describing the reshaping. This includes the influence of wave height and period, storm duration, berm width and elevation variations on the stability of berm breakwater with different armor stone sizes. A total of 222 tests have been performed to cover the impact of these parameters. According to the present research, one can observe that considering different armor stone sizes, berm width is a significant parameter concerning reshaping of a berm breakwater that has not been covered in previous works, so that as the berm width increases the amount of berm recession decreases. To assess the validity of the present formula, comparisons are made between the estimated berm recessions by this formula and formulae given by other researchers, showing that the estimation procedure foretells berm recession well according to the present data. It is observed that the recession estimated by the present formula has comparatively better correlation with the present experimental data, and also with other experimental results within the range of parameters tested.     

An experimental study on the parameterization of reshaped seaward profile of berm breakwaters

Berm breakwaters are rubble mound structures in which the seaward slope of the initial profile may be reshaped to become more stable under severe wave attack. The stones in the seaward slope move from the initial slope to an equilibrium profile. A 2D experimental study has been carried out in a wave flume at a hydraulic laboratory of Tarbiat Modares University to study the effects of sea state and structural parameters on the reshaped profile parameters of such breakwaters. A series of 287 tests have been performed to cover the effect of various sea state conditions such as wave height, wave period, number of waves and water depth at the toe of the structure, and structural parameters such as berm width, berm elevation above still water level and armor stone size. All the tests have been done employing irregular waves with a JONSWAP spectrum. In this paper, first the reshaped profiles are schematized, and then the key parameters of the reshaped seaward profiles such as step height, step length and depth of intersection point of initial and reshaped profile are investigated, using results of this experimental work. Eventually, formulae that include some sea state and structural parameters are derived for estimation of the reshaped profile parameters. To assess the validity of the proposed formulae, comparisons are made between the estimated parameters of reshaped profiles by these formulae and earlier formulae given by other researchers. The comparisons show that the estimation procedure foretells reshaping parameters well and with less scatter according to the present data and also other experimental results within the range of parameters tested.     

Wave run-up on bermed coastal structures

Reliable estimation of wave run-up is required for the effective and efficient design of coastal structures when flooding or wave overtopping volumes are an important consideration in the design process. In this study, a unified formula for the wave run-up on bermed structures has been developed using collected and existing data. As data on berm breakwaters was highly limited, physical model tests were conducted and the run-up was measured. Conventional governing parameters and influencing factors were then used to predict the dimensionless run-up level with 2% exceedance probability. The developed formula includes the effect of water depth which is required in understanding the influence of sea level rise and consequent changes of wave height to water depth ratio on the future hydraulic performance of the structures. The accuracy measures such as RMSE and Bias indicated that the developed formula is more accurate than the existing formulas. Additionally, the new formula was validated using field measurements and its superiority was observed when compared to the existing prediction formulas. Finally, the new design formula incorporating the partial safety factor was introduced as a design tool for engineers.     

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.     

风浪状态对海面粗糙度影响

风浪状态参数常用于对海面粗糙度的参数化。中等风速条件下考虑风浪状态参数影响的海面粗糙度参数化方案常存在自相关效应,本文通过分析实测数据得到了无量纲粗糙度随波陡变化的参数化方案,该方案能够有效去除自相关效应;高风速下风浪状态对海面粗糙度仍存在影响,文中基于新得出的中等风速下的海面粗糙度参数化方案,考虑海面飞沫悬浮层的影响,建立了适用于高风速条件下的海面粗糙度参数化方案,该海面粗糙度方案同样考虑了波陡的作用,将该方案计算出的理论值与实测数据进行比对,发现随着波陡的变化,理论值基本涉及测量值的覆盖范围,说明新建立的高风速条件下海面粗糙度方案对海面风浪状态具有较好的敏感性,且该方案能够较合理地描述海气界面之间动量传输。将新提出的适用于高风速下的海面粗糙度方案加入到海浪数值模式中,模拟飓风Ivan产生的台风浪,利用浮标数据进行验证,结果显示模拟的有效波高相对模式默认方案具有较高的精度,说明采用本文新建立的适合高风速的海面粗糙度方案能够改进海浪模式的台风浪有效波高模拟结果。     

Prediction of berm geometry using a set of laboratory tests combined with teaching–learning-based optimization and artificial bee colony algorithms

Understanding sediment movement in coastal areas is crucial in planning the stability of coastal structures, the recovery of coastal areas, and the formation of new coast. Accretion or erosion profiles form as a result of sediment movement. The characteristics of these profiles depend on the bed slope, wave conditions, and sediment properties. Here, experimental studies were performed in a wave flume with regular waves, considering different values for the wave height (H₀), wave period (T), bed slope (m), and mean sediment diameter (d₅₀). Accretion profiles developed in these experiments, and the geometric parameters of the resulting berms were determined. Teaching–learning-based optimization (TLBO) and artificial bee colony (ABC) algorithms were applied to regression functions of the data from the physical model. Dimensional and dimensionless equations were found for each parameter. These equations were compared to data from the physical model, to determine the best equation for each parameter and to evaluate the performances of the TLBO and ABC algorithms in the estimation of the berm parameters. Compared to the ABC algorithm, the TLBO algorithm provided better accuracy in estimating the berm parameters. Overall, the equations successfully determined the berm parameters.     

最大熵原理应用于海浪波高分布的研究

利用最大熵原理从理论上推导出波高的最大熵分布,在此基础上研究了状态参量对波高分布和波高熵的影响。影响最大熵分布的因子是平均波高和状态参量,不同海况对应的状态参量是不同的。利用波高实测资料,得出3种不同海况下的最大熵分布,通过比较发现最大熵分布很好地符合实测数据。把最大熵分布与目前广泛应用的瑞利分布作了比较,结果表明,最大熵分布有2个优点：没有对波高作出任何限制性假定和能够描述不同海况下的波高分布。     

Experimental Study of Wave Attenuation in Trapezoidal Floating Breakwaters

A comprehensive experimental study was carried out on the regular wave attenuation with a trapezoidal pontoontype floating breakwater(FB) in deep water. The functionalities of two simple FB geometries consist of a rectangle and a trapezoid with the slope of 60° were investigated under the wave attack. A two-dimensional wave flume was used in the experiment; the incident, transmitted waves, mooring line forces and motion responses of the floating breakwaters were measured. Also the influence of the sea state conditions(incident wave height and wave period)and structural parameters(draught of the structure) were investigated using the trapezoidal FB. Our experimental results indicated that the trapezoidal FB significantly reduced the wave transmission and mooring line force when compared with rectangular FBs. A new formula was developed in order to predict the value of the transmission coefficient in trapezoidal FBs with the slope of 60°. Experimental data showed to be consistent with the results of the formula.     

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.     

Weak dependence of the SWAN wave model on hydrodynamic properties of sea bottom

The third generation of the SWAN wave model is modified by the incorporation of new resistance laws for hydrodynamically rough, incompletely rough (smoothly rough), and smooth underlying surfaces. A modified model is used to determine the functional dependences of wave parameters (such as the dimensionless energy of waves and the dimensionless spectral peak frequency) on a dimensionless fetch. The results of calculations are compared to the experimental data obtained in Lake George (northeastern Australia), which has a nearly constant depth and extended, nearly rectilinear segments of coast. The SWAN model is shown to depend weakly on hydrodynamic properties of the sea bottom: distinctions arising from changes in hydrodynamic properties of the sea bottom are smaller than the variances of experimental estimates.     

An innovative block partition and equivalence method of the wave scatter diagram for offshore structural fatigue assessment

The fatigue assessment plays an increasing role for the offshore structural safety. Many fatigue assessment methods have been developed for this purpose. Among those methods, the time domain method is regarded as the most accurate method but less adopted in practice due to time consuming. In order to improve the efficiency of the time domain method, an innovative block partition and equivalence method of the wave scatter diagram is developed for offshore structural fatigue assessment. After the wave scatter diagram is partitioned into several blocks, the newly developed method, involves determination of the equivalent wave height, wave period and occurrence probability of the representative sea states based on modified energy equivalent principle. The equivalent wave period of the representative sea state is calculated via the spectral moment formula in which the equivalent spectral moments of zero and second order are obtained based on the weighted averaging principle. Combining with the determined wave period, the equivalent significant wave height can be determined by reversing the wave spectrum integral formula, where the equivalent wave energy of a divided block of the wave scatter diagram is modified by introducing a factor to compensate the effect of low- and high-amplitude cycles fatigue damage. The equivalent occurrence probability is equal to the summation of the original sea states’ occurrence probability within the divided block. The developed method has the advantage of preserving the stochastic characteristics of the short term sea states within the divided block during determining the representative sea state. At the same time the newly developed method has no limitation on block partition and can be applied on different offshore structure. Two structural models, a fixed mono-pile platform and a floating semi-submersible platform, are demonstrated in the numerical examples. Results indicate that the newly developed method is robust, computationally affordable, and accurate within engineering expectations.     

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.     

唐山近海海域波浪要素特征分析

本文基于唐山近海海域1#、2#浮标2017年4月至11 月实时海浪观测数据及部分风速风向数据, 对唐山近海海域波浪有效波高、有效波向、有效波周期等波参数特征进行了统计分析, 并利用origin 软件对波参数与风速、风向相关性进行了研究。研究结果表明： 1#、2# 浮标海域常浪向为SSW、SW、SSE, 常浪向有效波高均以0.2 ～ 0.4 m 小浪及3 ～ 4 s 短周期为主,有效波高1 m 以上较大波浪极少出现; 该海域波浪以风浪为主, 波浪破碎速度较快, 有效波高与风速相关性较强, 相关系数r 为0.71, 风向与波向、有效波高与周期基本无相关性, 该研究资料可为海上活动及防灾减灾提供技术依据。     

便携式高频地波雷达台湾海峡浪高观测

As an important equipment for sea state remote sensing, high frequency surface wave radar(HFSWR) has received more and more attention. The conventional method for wave height inversion is based on the ratio of the integration of the second-order spectral continuum to that of the first-order region, where the strong external noise and the incorrect delineation of the first- and second-order Doppler spectral regions due to spectral aliasing are two major sources of errors in the wave height. To account for these factors, two more indices are introduced to the wave height estimation, i.e., the ratio of the maximum power of the second-order continuum to that of the Bragg spectral region(RSCB) and the ratio of the power of the second harmonic peak to that of the Bragg peak(RSHB). Both indices also have a strong correlation with the underlying wave height. On the basis of all these indices an empirical model is proposed to estimate the wave height. This method has been used in a three-months long experiment of the ocean state measuring and analyzing radar, type S(OSMAR-S), which is a portable HFSWR with compact cross-loop/monopole receive antennas developed by Wuhan University since 2006. During the experiment in the Taiwan Strait, the significant wave height varied from 0 to 5 m. The significant wave heights estimated by the OSMAR-S correlate well with the data provided by the Oceanweather Inc. for comparison, with a correlation coefficient of 0.74 and a root mean square error(RMSE) of 0.77 m. The proposed method has made an effective improvement to the wave height estimation and thus a further step toward operational use of the OSMAR-S in the wave height extraction.     

Wave reflection by a vertical wall with a horizontal submerged porous plate

By applying the linear water wave theory and the eigenfunction expansion method, the wave reflection by a vertical wall with a horizontal submerged porous plate is investigated in this paper. The numerical results, concerning the effects of the dimensionless plate length, the relative water depth, and the porous effect parameter of the plate on the wave loads on the plate and the wave height near the wall as well as the reflection coefficient, are discussed. It is found that the submerged plate increases the complexity of the phenomenon related to the wave reflection and refraction in the close region of the wall, and leads to the occurrence of the phenomenon of wave trapping. The results indicate that there may exist a process of focusing wave energy near the wall for small dimensionless porous effect parameters, whereas the increase of the dimensionless porous effect parameter decreases gradually the wave height until setdown occurs. The behavior of a larger plate with proper porosity is similar to that of a wave absorber which can significantly suppress not only the wave height above the plate but also the reflection waves. The ability of the porous plate to reduce the wave height on the wall surface is, in general, directly proportional to the dimensionless plate length and may be strongest for a proper value of the dimensionless porous effect parameter. It is also demonstrated that the wave loads on a porous plate are smaller than those on an impermeable plate.     

Wave height parameter for damage description of rubble-mound breakwaters

In this paper it will be shown that the wave height parameter H₅₀, defined as the average wave height of the 50 highest waves reaching a rubble-mound breakwater in its useful life, can describe the effect of the wave height on the history of the armor damage caused by the wave climate during the structure's usable life.Using Thompson and Shuttler (Thompson, D.M., Shuttler, R.M., 1975. Riprap design for wind wave attack: A laboratory study on random waves. HRS Wallingford, Report 61, UK) data it will be shown that H₅₀ is the wave parameter that best represents the damage evolution with the number of waves in a sea state. Using this H₅₀ parameter, formulae as van der Meer (van der Meer, J.W., 1988. Rock slopes and gravel beaches under wave attack. PhD Thesis. Technical University of Delft) and Losada and Giménez-Curto (Losada, M.A., Gimenez–Curto, L.A., 1979. The joint effect of the wave height and period on the stability of rubble mound breakwaters using Iribarren's number. Coastal Engineering, 3, 77–96) are transformed into sea-state damage evolution formulae. Using these H₅₀-transformed formulae for regular and irregular sea states it will be shown how damage predictions are independent of the sea state wave height distribution.To check the capability of these H₅₀-formulae to predict damage evolution of succession of sea states with different wave height distributions, some stability tests with regular and irregular waves have been carried out. After analysing the experimental results, it will be shown how H₅₀-formulae can predict the observed damage independently of the sea state wave height distribution or the succession of sea states.     

Stability of berm breakwater with reduced armor stone weight

The basic principle involved in the design of S-shaped breakwater is the provision of a wide berm at or around the water level with smaller size armor stones than that used in conventional design, which are allowed to reshape till an equilibrium slope is achieved. An attempt is made to assess the influence of wave height, wave period, and berm width on the stability of S-shaped breakwater with reduced (30% reduction in armor stone weight) armor unit weight. From the investigation, it is found that the berm breakwater with 30% reduced armor weight would be stable for the design wave height if the berm width is 60 cm and wave period 1.2 s. For higher wave periods studied, zero damage wave height reduces by 20–40% of the design wave height. Wave period has large influence on the stability of berm breakwaters. The runup increases with decrease in weight up to W_o/W=0.9.     

Experimental and numerical investigations on the intact and damage survivability of a floating–moored oscillating water column device

This paper investigates the intact and damage survivability of a floating–moored Oscillating Water Column (OWC) device using physical model experiments and Computational Fluid Dynamics (CFD) simulations. Different extreme wave conditions have been tested using irregular and regular wave conditions. The device was moored to the tank floor via four vertical taut lines and the effect of the mooring line pre–tension on the device response was studied. It was found that the instantaneous position of the floating device was a key factor in the survivability analysis such that a certain irregular wave train that might not include the largest wave could induce the maximum response. Reducing the pre–tension minimized the maximum surge, but significantly increased the maximum tension due to mooring slack events causing snatch loads. A design regular wave with a period equal to the peak period and a height of 1.9–2.0 times the significant wave height could reasonably predict the same maximum line tension as the irregular sea state, but a smaller wave height was required to achieve the maximum surge. A single failure in the mooring system increased the maximum tension by 1.55 times the intact tension. For a damaged mooring system, using the same design regular wave condition derived from the survivability analysis with an intact mooring system could result in overestimating the maximum tension by more than 20% in comparison to the tension from the irregular sea state, but a smaller regular wave height or a different regular wave condition representing another sea state could lead to the same maximum tension. This highlighted the importance of investigating survival conditions with a damaged mooring system instead of simply using the same conditions derived for the intact mooring system.     

卷破波作用下沙质岸滩剖面形态判别式初探

通过波浪水槽实验,开展不同类型波浪作用下的沙质岸滩演化规律研究工作。本次实验研究不考虑比尺,采用1:10与1:20组成的复合沙质斜坡对岸滩进行概化,选取规则波和椭圆余弦波两种典型波浪作用,对波浪的传播、变形和破碎、上爬、回落过程以及波浪作用前后沙质岸滩床面地形进行了观测,探讨波浪作用下沙质岸滩剖面演化规律。本文实验工况中,规则波作用下,岸滩剖面呈现出沙坝剖面和滩肩剖面,椭圆余弦波作用下的岸滩剖面均呈滩肩形态,发现岸滩剖面形态不仅与波浪作用类型、强度、周期等因素相关,还与波浪破碎的强度等因素有关。通过对实验过程中现象的进行观察和分析,引入了卷破波水舌冲击角的概念。对波浪卷破破碎后形成的水流挟沙运动与岸滩剖面形态的关系进行定性分析,对水舌冲击角与Irribarren参数之间的关系进行定量分析,基于Irribarren参数与岸滩剖面形态的关系初步建立了波浪作用下沙质岸滩剖面形态判别关系式。通过本文实验结果和前人实验结果对趋势线进行拟合,求得其判别系数,判别式能够较好地划分淤积型岸滩、侵蚀型岸滩及过渡型岸滩三种岸滩形态。