Stone mobility and longshore transport at reshaping breakwaters

Physical model tests have been performed in two different wave flumes to analyse the threshold of stone movement and quantify the frequency and length of displacements due to head-on wave attacks at a reshaping breakwater. Data on stone movements were obtained from the observation of cumulative displacements at the end of each wave attack and from video records during the attack. Threshold conditions, frequency of movement and displacement length are expressed as function of a suitably modified stability number.A simple model is defined relating longshore transport due to oblique wave attack to stone mobility. The transport model is based on the assumption that movement statistics is affected by obliquity only through the appropriate mobility index and that stones move during up- and down-rush in the direction of incident and reflected waves. Without any calibration, results compare favourably with experimental data available in literature in the range of low mobility conditions where movement statistics was observed. A calibration is provided in order to obtain an accurate transport formula valid in a wide mobility range i.e. for reshaping breakwaters and up to gravel beaches.     

Effect of bed roughness on turbulent boundary layer and net sediment transport under asymmetric waves

This paper presents an investigation of the roughness effects in the turbulent boundary layer for asymmetric waves by using the baseline (BSL) k–ω model. This model is validated by a set of the experimental data with different wave non-linearity index, N_i (namely, N_i = 0.67, N_i = 0.60 and N_i = 0.58). It is further used to simulate asymmetric wave velocity flows with several values of the roughness parameter (a_m/k_s) which increase gradually, namely from a_m/k_s = 35 to a_m/k_s = 963. The effect of the roughness tends to increase the turbulent kinetic energy and to decrease the mean velocity distribution in the inner boundary layer, whereas in the outer boundary layer, the roughness alters the turbulent kinetic energy and the mean velocity distribution is relatively unaffected. A new simple calculation method of bottom shear stress based on incorporating velocity and acceleration terms is proposed and applied into the calculation of the rate of bed-load transport induced by asymmetric waves. And further, the effect of bed roughness on the bottom shear stress and bed-load sediment transport under asymmetric waves is examined with the turbulent model, the newly proposed method, and the existing calculation method. It is found that the higher roughness elements increase the magnitude of bottom shear stress along a wave cycle and consequently, the potential net sediment transport rate. Moreover, the wave non-linearity also shows a big impact on the bottom shear stress and the net sediment transport.     

The stability of the antifer units used on breakwaters in case of irregular placement

The primary aim of the study is to experimentally investigate the stability performance of antifer units on the trunk section of breakwaters under the effect of regular and irregular waves in case of irregular placement. The stability performance tests were conducted for different slopes, i.e. cot α=1.25, 1.5, 2.0, 2.5, under irregular waves and for cot α=2.5 under regular waves. Hudson’s formula was employed in order to characterize the stability performance of antifer units for the irregular placement technique. Different representative wave height parameters, i.e. H_s, H_1/10 and H_max, were examined to determine the one best characterizing breakwater stability. Furthermore, the effects of wave period and wave steepness on the stability of the breakwater were explored.     

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.     

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.     

Application of importance sampling method in sliding failure simulation of caisson breakwaters

It is assumed that the storm wave takes place once a year during the design period, and N histories of storm waves are generated on the basis of wave spectrum corresponding to the N-year design period. The responses of the breakwater to the N histories of storm waves in the N-year design period are calculated by mass-spring-dashpot mode and taken as a set of samples. The failure probability of caisson breakwaters during the design period of N years is obtained by the statistical analysis of many sets of samples. It is the key issue to improve the efficiency of the common Monte Carlo simulation method in the failure probability estimation of caisson breakwaters in the complete life cycle. In this paper, the kernel method of importance sampling, which can greatly increase the efficiency of failure probability calculation of caisson breakwaters, is proposed to estimate the failure probability of caisson breakwaters in the complete life cycle. The effectiveness of the kernel method is investigated by an example. It is indicated that the calculation efficiency of the kernel method is over 10 times the common Monte Carlo simulation method.     

Stability of rubble-mound breakwater using H50 wave height parameter

The prediction of rubble mound breakwaters' stability is one of the most important issues in coastal and maritime engineering. The stability of breakwaters strongly depends on the wave height. Therefore, selection of an appropriate wave height parameter is very vital in the prediction of stability number. In this study, H₅₀, the average of the 50 highest waves that reach the breakwater in its useful life, was used to predict the stability of the armor layer. First, H₅₀ was used instead of the significant wave height in the most recent stability formulas. It was found that this modification yields more accurate results. Then, for further improvement of the results, two formulas were developed using model tree.To develop the new formulas, two experimental data sets of irregular waves were used. Results indicated that the proposed formulas are more accurate than the previous ones for the prediction of the stability parameter. Finally, the proposed formulas were applied to regular waves and a wide range of damage levels and it was seen that the developed formulas are applicable in these cases as well.     

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.     

Shoreline response to a single shore-parallel submerged breakwater

Submerged breakwaters (SBWs) are becoming a popular option for coastal protection, mainly due to their low aesthetic impact on the natural environment. However, SBWs have rarely been employed for coastal protection in the past and therefore, their efficacy remains largely unknown. The main objective of the present study was to investigate the structural and environmental conditions that govern the mode of shoreline response (i.e shoreline erosion vs shoreline accretion) to SBWs. The relative importance of the key structural and environmental parameters governing the response mode to a single shore parallel SBW is investigated through a combination of theoretical analysis and numerical modelling. Using physical considerations, a theoretical response-function model is derived under several simplifying assumptions including parallel depth contours, linear wave theory, shore normal waves, and no wave–current interaction. Numerical modelling is undertaken with the Mike21 model suite to simulate the depth averaged velocity fields (without morphological updating) due to waves acting on a single shore-parallel SBW located on a schematised beach with parallel depth contours. In total 92 coupled wave–current simulations were undertaken. The results indicate that the mode of shoreline response to the SBW can be expressed in terms of the two non-dimensional parameters h_B/H₀ and (s_B/h_B)^3/2(L_B/h_B)²(A³/h_B)^1/2 (variables defined in the text).     

Modelling of sand transport under wave-generated sheet flows with a RANS diffusion model

A 1DV-RANS diffusion model is used to study sand transport processes in oscillatory flat-bed/sheet flow conditions. The central aim is the verification of the model with laboratory data and to identify processes controlling the magnitude and direction (‘onshore’/‘offshore’) of the net time-averaged sand transport. The model is verified with a large series of measured net sand transport rates, as collected in different wave tunnels for a range of wave-current conditions and grain sizes. Although not all sheet flow details are represented in the 1DV-model, it is shown that the model is able to give a correct representation of the observed trends in the data with respect to the influence of the velocity, wave period and grain diameter. Also detailed mean sediment flux profiles in the sheet flow layer are well reproduced by the model, including the direction change from ‘onshore’ to ‘offshore’ due to a difference in grain size from 0.34 mm (medium sand) to 0.13 mm (fine sand). A model sensitivity study with a selected series of net transport data shows that the stirring height of the suspended sediment ε_s/w_s strongly controls the magnitude and direction of the net sediment transport. Inclusion of both hindered settling and density stratification appears to be necessary to correctly represent the sand fluxes for waves alone and for waves + a superimposed current. The best agreement with a large dataset of net transport measurements is obtained with the 1DV-RANS model in its original settings using a Prandtl–Schmidt number σ_ρ = 0.5.     

Sediment transport and beach morphodynamics induced by free long waves,bound long waves and wave groups

New laboratory data are presented on the influence of free long waves, bound long waves and wave groups on sediment transport in the surf and swash zones. As a result of the very significant difficulties in isolating and identifying the morphodynamic influences of long waves and wave groups in field conditions, a laboratory study was designed specifically to enable measurements of sediment transport that resolve these influences. The evolution of model sand beaches, each with the same initial plane slope, was measured for a range of wave conditions, firstly using monochromatic short waves. Subsequently, the monochromatic conditions were perturbed with free long waves and then substituted with bichromatic wave groups with the same mean energy flux. The beach profile changes and net cross-shore transport rates were extracted and compared for the different wave conditions, with and without long waves and wave groups. The experiments include a range of wave conditions, e.g. high-energy, moderate-energy, low-energy waves, which induce both spilling and plunging breakers and different turbulent intensities, and the beaches evolve to form classical accretive, erosive, and intermediate beach states. The data clearly demonstrate that free long waves influence surf zone morphodynamics and promote increased onshore sediment transport during accretive conditions and decreased offshore transport under erosive conditions. In contrast, wave groups, which can generate both forced and free long waves, generally reduce onshore transport during accretive conditions and increase offshore transport under erosive conditions. The influence of the free long waves and wave groups is consistent with the concept of the relative fall velocity, H/w_sT, as a dominant parameter controlling net beach erosion or accretion. Free long waves tend to reduce H/w_sT, promoting accretion, while wave groups tend to increase the effective H/w_sT, promoting erosion.     

Placement Effect on the Stability of Tetrapod Armor Unit on Breakwaters in Irregular Waves

Tetrapod, one of the well-known artificial concrete units, is frequently used as an armor unit on breakwaters. Two layers of tetrapod units are normmaly placed on the breakwaters with different placement methods. In this study, the stability of tetrapod units with two different regularly placement methods are investigated experimentally in irregular waves. Stability coefficients of tetrapod units for both placement methods are obtained. The important characteristic wave parameters of irregular waves causing the same damage ratio as those of the regular waves are also determined. It reveals that the average of one-tenth highest wave heights within the wave train (H_1/10) causes the similar damage as regular waves.     

Prediction of geometrical properties of perfect breaking waves on composite breakwaters

Breaking wave loads on coastal structures depend primarily on the type of wave breaking at the instant of impact. When a wave breaks on a vertical wall with an almost vertical front face called the “perfect breaking”, the greatest impact forces are produced. The correct prediction of impact forces from perfect breaking of waves on seawalls and breakwaters is closely dependent on the accurate determination of their configurations at breaking. The present study is concerned with the determination of the geometrical properties of perfect breaking waves on composite-type breakwaters by employing artificial neural networks. Using a set of laboratory data, the breaker crest height, h_b, breaker height, H_b, and water depth in front of the wall, d_w, from perfect breaking of waves on composite breakwaters are predicted using the artificial neural network technique and the results are compared with those obtained from linear and multi-linear regression models. The comparisons of the predicted results from the present models with measured data show that the h_b, H_b and d_w values, which represent the geometry of waves breaking directly on composite breakwaters, can be predicted more accurately by artificial neural networks compared to linear and multi-linear regressions.     

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.     

On the stability criterion for fracture in dolos-armoured breakwaters

A new empirical stability criterion for dolos-armoured, rubble-mound breakwaters is proposed. This criterion is based on an analysis of the energy level at which dolos armour units fracture and break in a breakwater environment. The input information has been obtained from ten different prototype breakwaters. The present analysis indicates the ratio of the wave energy to size (mass) of the armour units at which dolos units break.     

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.     

Hydrodynamic efficiency of partially immersed caissons supported on piles

The efficiency of the breakwater, which consists of caissons supported on two or three rows of piles, was studied using physical models. The efficiency of the breakwater is presented as a function of the transmission, reflection and the wave energy dissipation coefficients. Regular waves with wide ranges of wave heights and periods and constant water depth were used. Different characteristics of the caisson structure and the supporting pile system were also tested. It was found that, the transmission coefficient (k_t) decreases with increasing the relative breakwater draft D/L, increasing the relative breakwater width B/h, and decreasing the piles gap-diameter ratio G/d. It is possible to achieve k_t values less than 0.25 when D/L≥0.1. The reflection coefficient takes the opposite trend especially when D/L≤0.15. The proposed breakwater dissipates about 10-25% of the incident wave energy. Also, simple empirical equations are developed for estimating the wave transmission and reflection. In addition, the proposed breakwater model is efficient compared with other floating breakwaters.     

Analysis of temporal and spatial characteristics of waves in the Indian Ocean based on ERA-40 wave reanalysis

Based on the 45-year (09/1957-08/2008) European Centre for Medium-Range Weather Forecasts (ECMWF) Reanalysis (ERA-40) wave reanalysis dataset, this study analyzes interannual and interdecadal variabilities and intraseasonal oscillations of sea surface wind speed (WS), wind sea wave height (H^w), swell wave height (H^s) and significant wave height (H_s) in the Roaring Forties and tropical waters of the Indian Ocean, to determine swell propagation characteristics. The results show: (1) monthly variabilities of H^s in the Roaring Forties are in good agreement with those in tropical waters of the Indian Ocean; swell plays a dominant role in mixed waves throughout most of the Indian Ocean; and WS, H^w, H^s, and H_s exhibit a significant increasing trend over the 45-year study period. (2) H^s in the Roaring Forties and tropical waters of the Indian Ocean share a common period of 9.8–10.4 years on an interdecadal scale; and WS and H^s in the Roaring Forties and H^s in the tropical waters of the Indian Ocean share a common period of approximately 8 days (weekly oscillation) on an intraseasonal scale. (3) Swell of the Roaring Forties needs approximately 30 h to fully respond to the wind in this region. Approximately 84 h are required for H^s to propagate from the Roaring Forties to the tropical waters of the south Indian Ocean, while it takes approximately 132–138 h for H^s to propagate from the Roaring Forties to the tropical waters of the north Indian Ocean.