A new formula for the sea state and structural parameters influencing the stability of homogeneous reshaping berm breakwaters

The berm recession of a reshaping berm breakwater has a very important role for the stability of this kind of structure. Based on a 2D experimental modeling method in a wave flume, the recession of the berm due to sea state and structural parameters has been studied. Irregular waves with a JONSWAP spectrum were used. A total of 215 tests have been performed 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. In this paper, first a new dimensionless parameter is introduced to evaluate the combined effect of wave height and wave period on berm recession using results of the experimental work. Then, a formula that includes some sea state and structural parameters is derived using the new dimensionless parameter for estimating the berm recession. A comparison is made between the estimated berm recessions by this new formula and formulae given by other researchers to show the preference of using the new dimensionless parameter. The comparison shows that the recession estimated by the new formula has not only a better correlation with the present experimental data, but also has an improved correlation with other experimental results within the range of parameters tested. Outside the range of parameters tested the Lykke Andersen (2006) formula performed best.     

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.     

Shear strength of soil berm during lateral buckling of subsea pipelines

The soil resistance developed during temperature- and pressure-induced large lateral movements of shallowly embedded subsea flowlines is an important input parameter for the structural design process. A major source of uncertainty in calculation of the soil resistance is the undrained shear strength of the soil berm produced as the flowline moves across the seabed, which is affected by the level of remoulding. To investigate the effect of pipeline embedment and displacement amplitude on the shear strength of the berm, a set of centrifuge model tests was conducted on kaolin clay, involving laterally moving pipelines with constant embedments in the range 5%–35% of the pipe diameter. Back-analysis of the test results, using finite element limit analysis, showed that the shear strength of the soil berm is a function of pipe displacement amplitude, pipe embedment, and soil sensitivity. On the basis of these results, we propose that the overall berm undrained shear strength may be determined as a convolution of the shear strengths of its constituent soil elements. Finally, a formula is presented for calculating the shear strength of soil elements within the soil berm, and this is used to back-analyse the overall soil berm resistance from the model tests.     

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.     

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.     

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.     

Appraisal of storm beach buffer width for cyclonic waves

The loss of beach sand from berm and dune due to high waves and surge is a universal phenomenon associated with sporadic storm activities. To protect the development in a coastal hazard zone, hard structures or coastal setback have been established in many countries around the world. In this paper, the requirement of a storm beach buffer, being a lesser extent landward comparing with the coastal setback to ensure the safety of infrastructures, is numerically assessed using the SBEACH model for three categories of wave conditions in terms of storm return period, median sand grain size, berm width, and design water level. Two of the key outputs from the numerical calculations, berm retreat and bar formation offshore, are then analysed, as well as beach profile change. After having performed a series of numerical studies on selected large wave tank (LWT) test results with monochromatic waves using SBEACH, we may conclude that: (1) Berm erosion increases and submerged bar develops further offshore as the storm return period increases for beach with a specific sand grain size, or as the sand grain reduces on a beach under the action of identical wave condition; (2) Higher storm waves yield a large bar to form quicker and subsequently cause wave breaking on the bar crest, which can reduce the wave energy and limit the extent of the eroding berm; (3) A larger buffer width is required for a beach comprising small sand grain, in order to effectively absorb storm wave energy; and (4) Empirical relationships can be tentatively proposed to estimate the storm beach buffer width, from the input of wave conditions and sediment grain size. These results would benefit a beach nourishment project for shore protection or design of a recreational beach.     

陡墙式海堤平台对波浪爬高影响

通过物理模型试验研究陡墙式海堤复坡平台高程和宽度对波浪爬高的影响。平台越宽对波浪爬高影响越大,平台位于静水位处对波浪爬高影响最大,并得出了受平台影响的波浪爬高折减系数计算公式,可供工程参考使用。     

Effect of Berm Width and Elevation on Irregular Wave Run-Up

This paper discusses the effect of berm width and elevation of composite slope on irregular wave run-up. Based on the data obtained from model tests, the formula and distribution of irregular wave run-up on composite slope are derived. The changing of wind speed, width and elevation of the berm are considered comprehensively. The wave run-up with various exceedance probability can be es-timated utilizing the distribution curves of irregular wave run-up.     

Geometrical properties of perfect breaking waves on composite breakwaters

The experimental results have so far shown that when a wave breaks on a vertical wall with an almost vertical front face at the instant of impact that is called perfect breaking or perfect impact, the greatest impact forces are produced on the wall. Therefore, the configuration of breaking waves is important in the design considerations of coastal structures. The present study is concerned with determining the geometrical properties of oscillatory waves that break perfectly on the vertical wall of composite-type breakwaters. The laboratory tests for perfect breaking waves on composite breakwaters are conducted with base slopes of 1/2, 1/4 and 1/6, and with berm widths of 0.00, 0.10, 0.20, 0.30 and 0.40 m. The shape and the dimensions of waves at the instant of perfect breaking on the wall are determined using a video camera. The experimental results for the geometrical properties of the breakers are presented non-dimensionally. Within the range of present experimental conditions, it is found that the dimensionless breaker crest height, h_b/d_w, and dimensionless breaker height, H_b/d_w, decrease; and, dimensionless breaker depth, d_w/H₀, increases with increasing relative berm width, B/D. The breaker height index, H_b/H₀, is almost unaffected by B/D. The deep-water wave steepness and the base slope of the breakwater do not seem to influence the geometrical properties of the breakers at wall systematically.     

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.     

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 stability of rubble mound breakwaters with a berm

Breakwaters with a berm can significantly reduce overtopping and reduce the required rock size compared to straight slopes without a berm. Here, the stability of rock slopes with a horizontal berm has been studied by means of physical model tests to provide information on the required rock size. The tests and analysis are focussed on the slope above the berm as well as the slope below the berm. Also the stability of the rock at the berm is addressed. The influence of the slope angle (1:2 and 1:4), the width of the berm, the level of the berm, and the wave steepness has been investigated. Based on the test results prediction formulae have been derived to quantify the required rock size for rubble mound breakwaters with a berm. Especially for the slope above the berm, the rock size can be reduced significantly compared to straight slopes.     

Predictions on Irregular Wave run-up and Overtopping

A series of hydraulic model tests are carried out to investigate random wave run-up and overtopping on smooth, impermeable single slope and composite slope. Based on analysis of the influences of wave steepness, structure slope, incident wave angle, width of the berm and water depth on the berm and the wave run-up, empirical formulas for wave run-up on dike are proposed. Moreover, empirical formula on estimating the wave run-up on composite slope with multiple berms is presented for practical application of complex dike cross-section. The present study shows that the influence factors for wave overtopping are almost the same as those for wave run-up and the trend of the wave overtopping variation with main influence parameters is also similar to that for wave run-up. The trend of the wave overtopping discharge variations can be well described by two main factors, i.e. the wave run-up and the crest freeboard of the structure. A new prediction method for wave overtopping discharge is proposed for random waves. The proposed prediction formulas are applied to case study of over forty cases and the results show that the prediction methods are good enough for practical design purposes.     

Wave reflection from coastal structures in design conditions

Based on an extensive database of more than 4000 data, this paper analyses wave reflection for various types of coastal structures in design conditions, such as smooth, rock and armour unit slopes. A new simple formula has been developed that relates the reflection coefficient to the breaker parameter and seems to fit all kinds of revetment materials by changing two coefficients. These coefficients depend only on the correct roughness factor, provided by recent research on overtopping discharges. The effects on reflection due to composite slopes and to low crests are also examined and proper extensions of the formula are provided.     

Calculation of beach change under interacting cross-shore and longshore processes

This paper presents a mathematical approach and numerical model that simulates beach and dune change in response to cross-shore processes of dune growth by wind and dune erosion by storms, and by gradients in longshore sand transport that will alter shoreline position. Sub-aerial transport processes are represented, whereas sub-aqueous transport is neglected. The system is tightly coupled morphologically, with the berm playing a central role. For example, the potential for sand to be transported to the dune by wind depends on berm width, and sand lost in erosion of the dune during storms can widen the berm. Morphologic equilibrium considerations are introduced to improve reliability of predictions and stability of the non-linear model. An analytical solution is given under simplification to illustrate properties of the model. Sensitivity tests with the numerical solution of the coupled equations demonstrate model performance, with one test exploring beach and dune response to potential increase in storm-wave height with global warming. Finally, the numerical model is applied to examine the consequences of groin shortening at Westhampton Beach, Long Island, New York, as an alternative for providing a sand supply to the down-drift beach. Results indicate that the sand will be released over several decades as the shoreline and dune move landward in adjustment to the new equilibrium condition with the shortened groins.     

Singular points at berm breakwaters: scale effects, rear, round head and longshore transport

Design aspects other than the profile development of the seaward side have been investigated in this paper. Aspects such as scale effects, rear stability, round head design and longshore transport have been treated here, based on extensive test series on two different berm breakwater designs. A first conclusion is that scale effects were not present in a 1:35 scale model compared with a 1:7 large scale model with wave heights up to 1.7 m.A first design rule was assessed on the relationship between damage at the rear of a berm breakwater and the crest height, wave height, wave steepness and rock size. Tests on a berm breakwater head showed that enlarging the berm height at the crest and therefore the amount of rock in the berm was effective with regard to stability.Finally the onset of longshore transport due to oblique wave attack was studied and compared with literature. Formulae were derived for this onset of transport and also for the range of more serious transport up to longshore transport of coarse gravel.     

Toe Structure Stability of Sloping Breakwater

1 .IntroductionTheslopingbreakwateriswidelyusedintheprotectionofcoastalstructures ,withrubblemoundtoebermbuiltatthefootofthewave attackingslope .Thefunctionofarubblemoundtoestructureis ,inadditiontodecreasingthequantityofmainarmorstoneused ,toprovidestaticsupporttothemainarmorlayer,avoidingtherollingdownofmainarmorstonesandprotectingtheapronstonesfromero sion .TheweightoftoebermstonesisdecidedaccordingtotheCodeofBreakwaterDesignandBuildingformulatedbytheMinistryofCommunicationsofChina .When…     

Mathematical modeling of soil mixture flow surge and its application to coastal area

The purpose of this study is to investigate debris flow surge that is set up with a numerical model using governing equations applied by the dynamics of a liquid–solid mixture. This model is performed by applying the finite difference method to display elapses of time. To measure the behavior mechanisms of the debris flow surge, the following are analyzed: the flow discharge, flow depth, and sediment volume concentration at the end of downstream channel. The flow discharge and flow depth only surge right after the debris flow reaches the downstream channel as the berm width shortens. In contrast, as the berm width lengthens, the flow discharge and water flow recede. As the berm width decreases, the sediment concentration shows a high concentration and a great height difference at the inflection point. Vice versa, when the berm width increases, an inflection point can be seen, but it reveals a low concentration and a low height difference. The numerical model of this study was applied to the coast of South Korea and analyzed. This study will provide information in predicting disasters caused by debris flow and in planning for various counter measures to prevent disasters.