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Keywords = mound breakwaters

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19 pages, 4479 KiB  
Article
Reducing Wave Overtopping on Rubble Mound Breakwaters Using Floating Kelp Farms
by Filipe Miranda, Tomás Calheiros-Cabral, Diogo Mendes, Paulo Rosa-Santos, Francisco Taveira-Pinto and Tiago Fazeres-Ferradosa
J. Mar. Sci. Eng. 2025, 13(5), 850; https://doi.org/10.3390/jmse13050850 - 25 Apr 2025
Viewed by 628
Abstract
Near-surface floating kelp farms constitute a Nature-Based Solution (NBS) capable of damping incident wind-generated waves, which might be beneficial to reduce wave overtopping on maritime structures. As the global mean sea level rises, the mean wave overtopping discharge is expected to increase. The [...] Read more.
Near-surface floating kelp farms constitute a Nature-Based Solution (NBS) capable of damping incident wind-generated waves, which might be beneficial to reduce wave overtopping on maritime structures. As the global mean sea level rises, the mean wave overtopping discharge is expected to increase. The incorporation of this NBS, as a green–grey solution, might be beneficial to mitigate this effect. Physical modelling experiments with random waves have been conducted to assess the ability of this NBS to reduce the mean wave overtopping discharge on a rubble mound breakwater. Results show that while the mean wave overtopping discharge was reduced by 47% with a kelp farm length of 50 m (prototype scale), a kelp farm of 200 m achieved a reduction of 93% for the tested conditions. This reduction is mainly a function of the ratio between floating kelp farm length and incident wavelength. An idealized case study at the Port of Leixões breakwater suggests that, under storm wave conditions with return period of 2 and 5 years, floating kelp farms could maintain mean wave overtopping discharges below present levels until 2070. Thus, this study highlights the relevance of incorporating NBS with existing coastal and port defence structures as an adaptation measure to mitigate climate change effects. Full article
(This article belongs to the Section Coastal Engineering)
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24 pages, 8275 KiB  
Article
Design of Portable Reefs to Protect Young Mangroves
by Hiroshi Takagi, Farhat Tahsin Prattoyee, Jun Mitsui and Shin-ichi Kubota
J. Mar. Sci. Eng. 2025, 13(4), 734; https://doi.org/10.3390/jmse13040734 - 6 Apr 2025
Viewed by 754
Abstract
For a successful mangrove plantation, previous studies have proposed a small rubble mound breakwater, termed a “portable reef”, and explored the effectiveness of such reefs in terms of wave transmission. This study conducted a real-scale wave flume experiment incorporating a portable reef to [...] Read more.
For a successful mangrove plantation, previous studies have proposed a small rubble mound breakwater, termed a “portable reef”, and explored the effectiveness of such reefs in terms of wave transmission. This study conducted a real-scale wave flume experiment incorporating a portable reef to assess the oscillatory behavior of young mangroves. To capture the dynamics of these young mangrove analogs—represented as elastic bodies—we employed a high-speed camera for precise tracking. A comparative analysis of the oscillatory characteristics was performed, evaluating the responses in both the presence and absence of the reef. The findings revealed several important points. First, portable reefs can effectively reduce wave heights, but they reduce plant oscillations to an even greater degree. Second, by calibrating the elastic modulus of the plant models, their oscillation behaviors can be analytically predicted. The results of our analytical model indicate that the acceleration experienced by the plants is amplified under conditions of shorter wave periods and softer stems, highlighting an increased susceptibility to damage from short-period waves, particularly in very young mangroves. Third, we identified that the conventional wave transmission formulas tend to overestimate the reduction in wave energy attributable to portable reefs, which consequently leads to an underestimation of the young mangroves’ oscillations. Based on these findings, we propose an integrated chart that combines wave transmission and plant oscillation coefficients, aimed at enhancing the design and effectiveness of portable reefs in protecting young mangroves. The insights obtained from this study will aid in the informed design of portable reefs. Full article
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24 pages, 14035 KiB  
Article
Analysis of Dynamic Changes in Sedimentation in the Coastal Area of Amir-Abad Port Using High-Resolution Satellite Images
by Ali Sam-Khaniani, Giacomo Viccione, Meisam Qorbani Fouladi and Rahman Hesabi-Fard
J. Imaging 2025, 11(3), 86; https://doi.org/10.3390/jimaging11030086 - 18 Mar 2025
Viewed by 602
Abstract
Sediment transport and shoreline changes causing shoreline morphodynamic evolution are key indicators of a coastal structure’s operational continuity. To reduce the computational costs associated with sediment transport modelling tools, a novel procedure based on the combination of a support vector machine for image [...] Read more.
Sediment transport and shoreline changes causing shoreline morphodynamic evolution are key indicators of a coastal structure’s operational continuity. To reduce the computational costs associated with sediment transport modelling tools, a novel procedure based on the combination of a support vector machine for image classification and a trained neural network to extrapolate the shore evolution is presented here. The current study focuses on the coastal area over the Amir-Abad port, using high-resolution satellite images. The real conditions of the study domain between 2004 and 2023 are analysed, with the aim of investigating changes in the shore area, shoreline position, and sediment appearance in the harbour basin. The measurements show that sediment accumulation increases by approximately 49,000 m2/y. A portion of the longshore sediment load is also trapped and deposited in the harbour basin, disrupting the normal operation of the port. Afterwards, satellite images were used to quantitatively analyse shoreline changes. A neural network is trained to predict the remaining time until the reservoir is filled (less than a decade), which is behind the west arm of the rubble-mound breakwaters. Harbour utility services will no longer be offered if actions are not taken to prevent sediment accumulation. Full article
(This article belongs to the Section AI in Imaging)
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18 pages, 4654 KiB  
Article
On-Site Stability Assessment of Rubble Mound Breakwaters Using Unmanned Aerial Vehicle-Based Photogrammetry and Random Sample Consensus
by Marcos Arza-García, José Alberto Gonçalves, Vladimiro Ferreira Pinto and Guillermo Bastos
Remote Sens. 2024, 16(2), 331; https://doi.org/10.3390/rs16020331 - 14 Jan 2024
Cited by 7 | Viewed by 2402
Abstract
Traditional methods for assessing the stability of rubble mound breakwaters (RMBs) often rely on 2.5D data, which may fall short in capturing intricate changes in the armor units, such as tilting and lateral shifts. Achieving a detailed analysis of RMB geometry typically requires [...] Read more.
Traditional methods for assessing the stability of rubble mound breakwaters (RMBs) often rely on 2.5D data, which may fall short in capturing intricate changes in the armor units, such as tilting and lateral shifts. Achieving a detailed analysis of RMB geometry typically requires fully 3D methods, but these often hinge on expensive acquisition technologies like terrestrial laser scanning (TLS) or airborne light detection and ranging (LiDAR). This article introduces an innovative approach to evaluate the structural stability of RMBs by integrating UAV-based photogrammetry and the random sample consensus (RANSAC) algorithm. The RANSAC algorithm proves to be an efficient and scalable tool for extracting primitives from point clouds (PCs), effectively addressing challenges presented by outliers and data noise in photogrammetric PCs. Photogrammetric PCs of the RMB, generated using Structure-from-Motion and MultiView Stereo (SfM-MVS) from both pre- and post-storm flights, were subjected to the RANSAC algorithm for plane extraction and segmentation. Subsequently, a spatial proximity criterion was employed to match cuboids between the two time periods. The methodology was validated on the detached breakwater of Cabedelo do Douro in Porto, Portugal, with a specific focus on potential rotations or tilting of Antifer cubes within the protective layer. The results, assessing the effects of the Leslie storm in 2018, demonstrate the potential of our approach in identifying and quantifying structural changes in RMBs. Full article
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10 pages, 769 KiB  
Technical Note
Influence of Van Gent Parameters on the Overtopping Discharge of a Rubble Mound Breakwater
by Federico Castiglione, Martina Stagnitti, Rosaria Ester Musumeci and Enrico Foti
J. Mar. Sci. Eng. 2023, 11(8), 1600; https://doi.org/10.3390/jmse11081600 - 16 Aug 2023
Cited by 2 | Viewed by 1221
Abstract
The choice of the values of the friction parameters may strongly influence the numerical modeling of the interaction between waves and porous media. Here, an assessment of such an influence is carried out using the OpenFOAM solver IhFoamV1 to simulate the response of [...] Read more.
The choice of the values of the friction parameters may strongly influence the numerical modeling of the interaction between waves and porous media. Here, an assessment of such an influence is carried out using the OpenFOAM solver IhFoamV1 to simulate the response of the Catania harbor breakwater under extreme wave attack. The numerical model was validated by comparison with an experimental dataset, and a sensitivity analysis of the overtopping discharge estimate to van Gent parameter β was carried out testing values suggested by previous studies. A discussion on the importance of a careful estimate of such a parameter when dealing with the numerical modeling of porous coastal structures is presented. Indeed, variations in the non-dimensional overtopping discharge higher than 150% were observed as a consequence of a small variation (1020%) in the absolute value of β. Full article
(This article belongs to the Special Issue Advanced Studies in Breakwaters and Coastal Protection)
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24 pages, 9003 KiB  
Article
Hydraulic Response and Overtopping Performance of Single-Layer Double Cube Unit Armored Mound Breakwater
by Iman Safari, Dominique Mouazé, Soroush Aliasgary, Guillaume Carpentier and François Ropert
J. Mar. Sci. Eng. 2023, 11(7), 1382; https://doi.org/10.3390/jmse11071382 - 6 Jul 2023
Cited by 4 | Viewed by 1974
Abstract
A newly developed friction-interlocking armor unit called the ‘Double cube’ (DC) was designed to improve the performance of a concrete armor unit used in river/marine structures against currents/waves actions. The DC unit is an octagonal-shaped block made up of two parts: an upper [...] Read more.
A newly developed friction-interlocking armor unit called the ‘Double cube’ (DC) was designed to improve the performance of a concrete armor unit used in river/marine structures against currents/waves actions. The DC unit is an octagonal-shaped block made up of two parts: an upper cube set on a lower base that is either square or octagonal in shape. The innovative design aims to provide good performance in terms of stability, to allow for high tolerance placement with various contact points, and to allow for ease of placement. The DC’s shape and placement enhance the unit’s stability by bringing the center of gravity closer to the underlayer and by providing a large contact surface with the surrounding blocks that reduces the chance of extraction and limits movements (rocking, lifting) via the “keystone” effect. The characteristics of this new unit provide a relatively high hydraulic stability number for the armor layer (NS = 2.9), a favorable hydraulic performance due to energy dissipation from turbulence and aeration, as well as a high roughness coefficient (γf ≈ 0.46), helping to reduce overtopping. Full article
(This article belongs to the Special Issue Advanced Studies in Breakwaters and Coastal Protection)
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19 pages, 2814 KiB  
Article
Wave Transmission over Rubble-Mound Submerged Breakwaters
by Elpidoforos Repousis, Ioannis Roupas and Constantine Memos
J. Mar. Sci. Eng. 2023, 11(7), 1346; https://doi.org/10.3390/jmse11071346 - 1 Jul 2023
Cited by 5 | Viewed by 2098
Abstract
This study focuses on the prediction of technical efficiency of narrow-crested submerged permeable rubble-mound breakwaters, in terms of wave attenuation. A number of existing formulae for estimating wave transmission coefficient for submerged breakwaters can be found in the literature, whereas in this work [...] Read more.
This study focuses on the prediction of technical efficiency of narrow-crested submerged permeable rubble-mound breakwaters, in terms of wave attenuation. A number of existing formulae for estimating wave transmission coefficient for submerged breakwaters can be found in the literature, whereas in this work further improvement for that estimation has been achieved mainly through physical modelling. A series of 2D experiments under scale were conducted for regular and random waves providing data on wave transmission coefficient and respective wave breaking characteristics. A Boussinesq-type wave model capable of simulating wave propagation for regular waves over porous submerged breakwaters was also used in order to provide additional wave transmission information. Data analysis showed that wave breaking mechanism significantly affects wave energy dissipation and, therefore, wave breaking occurrence and type can be directly linked to wave transmission coefficient for a given structure’s geometry and sea state. The result of this work is the proposal of a set of simple semi-empirical equations for predicting wave transmission coefficient over small profile porous submerged breakwaters in relevance to the parameterization of the expected dominant wave breaking mechanism. Full article
(This article belongs to the Special Issue Advanced Studies in Breakwaters and Coastal Protection)
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15 pages, 4691 KiB  
Article
On the Stability of Rubble Mound Structures under Oblique Wave Attack
by Meysam Bali, Amir Etemad-Shahidi and Marcel R. A. van Gent
J. Mar. Sci. Eng. 2023, 11(7), 1261; https://doi.org/10.3390/jmse11071261 - 21 Jun 2023
Cited by 2 | Viewed by 1833
Abstract
Slope stability formulae for rubble mound structures are usually developed for head-on conditions. Often, the effects of oblique waves are neglected, mainly because it is assumed that for oblique wave attack, the reduction in damage compared to perpendicular wave attack is insignificant. When [...] Read more.
Slope stability formulae for rubble mound structures are usually developed for head-on conditions. Often, the effects of oblique waves are neglected, mainly because it is assumed that for oblique wave attack, the reduction in damage compared to perpendicular wave attack is insignificant. When the incident waves are oblique, the required armour size can be reduced compared to the perpendicular wave attack case. Therefore, it is important to consider the wave obliquity influence on slope stability formulae as a reduction factor. One of the most recent formulae for estimating the stability of rock-armoured slopes, referred to as Etemad-Shahidi et al. (2020), was proposed for perpendicular wave attack. The aim of this study is to develop a suitable wave obliquity reduction factor for the above-mentioned stability formula. To achieve this, first, laboratory experiment datasets from existing reliable studies were selected and analysed. Then, previously suggested reduction factors were evaluated and a suitable reduction factor for the mentioned stability formula were suggested. The suggested reduction factor includes the effect of wave obliquity and directional spreading explicitly. It is shown that the stability prediction is improved by using the wave obliquity reduction factor. Full article
(This article belongs to the Special Issue Coastal Engineering: Sustainability and New Technologies, 2nd Edition)
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18 pages, 4956 KiB  
Article
Determining Wave Transmission over Rubble-Mound Breakwaters: Assessment of Existing Formulae through Benchmark Testing
by Nasrin Hassanpour, Diego Vicinanza and Pasquale Contestabile
Water 2023, 15(6), 1111; https://doi.org/10.3390/w15061111 - 14 Mar 2023
Cited by 6 | Viewed by 4033
Abstract
Low-crested and submerged breakwaters are frequently employed as coastal defence structures. Their efficiency is governed by wave energy dissipation, and the wave transmission coefficient can evaluate this parameter. The current study conducts experimental investigations on both low-crested and submerged breakwaters exposed to different [...] Read more.
Low-crested and submerged breakwaters are frequently employed as coastal defence structures. Their efficiency is governed by wave energy dissipation, and the wave transmission coefficient can evaluate this parameter. The current study conducts experimental investigations on both low-crested and submerged breakwaters exposed to different wave conditions to compare their performance with that of emerged breakwaters. The current study provides a comprehensive review of existing formulae and highlights the impact of design variables. To evaluate the reliability of each existing formula, four “reference” configurations are used. Having these structures at the same overall volume, the results also provide a useful tool for engineers involved in the lowering operation of existing breakwaters. Nature and magnitude of governing parameters are investigated, and some points of criticism are outlined. The comparison results show that few of the existing equations give reliable estimates of the transmission coefficient for all the models tested in this study. Higher values of root mean square error are related to the emerged breakwater rather than the submerged ones. To obtain information about the transmitted wave energy, spectral analysis is applied as well. Different behaviours of the transmitted spectrum, n terms of shape and peak frequency, are highlighted. The results improve the overall knowledge on formulae that are in the literature, in order to make the user more aware. Full article
(This article belongs to the Topic Coastal Development, Conservation and Sustainability)
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18 pages, 5210 KiB  
Article
Damage Evolution Prediction during 2D Scale-Model Tests of a Rubble-Mound Breakwater: A Case Study of Ericeira’s Breakwater
by Rute Lemos, João A. Santos and Conceição J.E.M. Fortes
Modelling 2023, 4(1), 1-18; https://doi.org/10.3390/modelling4010001 - 20 Dec 2022
Cited by 1 | Viewed by 2063
Abstract
Melby presents a formula to predict damage evolution in rubble-mound breakwaters whose armour layer is made of rock, based on the erosion measured in scale-model tests and the characteristics of the incident sea waves in such tests. However, this formula is only valid [...] Read more.
Melby presents a formula to predict damage evolution in rubble-mound breakwaters whose armour layer is made of rock, based on the erosion measured in scale-model tests and the characteristics of the incident sea waves in such tests. However, this formula is only valid for armour layers made of rock and for the range of tested sea states. The present work aims to show how the Melby methodology can be used to establish a similar formula for the armour layer damage evolution in a rubble-mound breakwater where tetrapods are employed. For that, a long-duration test series is conducted with a 1:50 scale model of the quay section of the Ericeira Harbour breakwater. The eroded volume of the armour layer was measured using a Kinect position sensor. The damage parameter values measured in the experiments are lower than those predicted by the formulation for rock armour layers. New ap and b coefficients for the Melby formula for the tested armour layer were established based on the minimum root mean square error between the measured and the predicted damage. This work shows also that it is possible to assess the damage evolution in scale-model tests with rubble-mound breakwaters by computing the eroded volume and subsequently, the dimensionless damage parameter based on the equivalent removed armour units. Full article
(This article belongs to the Special Issue Ocean and Coastal Modelling)
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11 pages, 2303 KiB  
Article
Laboratory Experiments on the Influence of the Wave Spectrum Enhancement Factor on a Rubble Mound Breakwater
by Hosny Bakali, Ismail Aouiche, Najat Serhir, Youssef Zahir, El hassan Ziane, Abderrazak Harti, Zakariae Zerhouni and Edward Anthony
J. Mar. Sci. Eng. 2022, 10(12), 2035; https://doi.org/10.3390/jmse10122035 - 19 Dec 2022
Cited by 1 | Viewed by 2453
Abstract
This paper experimentally explored the influence of the wave spectrum shape variation on breakwater design. The energy spectrum function generally considered for the design of coastal structures is the JONSWAP spectrum. The laboratory results were therefore used to assess the impact of changing [...] Read more.
This paper experimentally explored the influence of the wave spectrum shape variation on breakwater design. The energy spectrum function generally considered for the design of coastal structures is the JONSWAP spectrum. The laboratory results were therefore used to assess the impact of changing the spectrum shape parameter (PEF). We analysed armour stability and wave overtopping in a wave flume with a geometric similarity ratio of 1:30. The experimental results showed that the PEF has maximum influence on overtopping and wave pressures on the crown wall. For a PEF value of 3.3, overtopping was much higher (30% to 100% higher) than with a PEF of 1. Pressure on the crown wall was 20% higher with a PEF of 3.3 in comparison with that for a PEF equal to 1. The stability of the breakwater’s block armour is less sensitive to the PEF variation. Full article
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14 pages, 2214 KiB  
Article
Field Campaign on Pressure on the Crown Wall at the Outer Port of Punta Langosteira Breakwater
by José Sande, Maria Graça Neves, José-Santos López-Gutiérrez, M. Dolores Esteban, Andrés Figuero and Vicente Negro
J. Mar. Sci. Eng. 2022, 10(10), 1377; https://doi.org/10.3390/jmse10101377 - 26 Sep 2022
Cited by 1 | Viewed by 2275
Abstract
Punta Langosteira port, located in A Coruña (Spain), was monitored during the winters of 2017 and 2018, measuring wave pressure in the crown wall structure. Furthermore, the metocean variables were measured on a buoy located very close to the breakwater. This paper presents [...] Read more.
Punta Langosteira port, located in A Coruña (Spain), was monitored during the winters of 2017 and 2018, measuring wave pressure in the crown wall structure. Furthermore, the metocean variables were measured on a buoy located very close to the breakwater. This paper presents the real pressures measured at the crown wall of the breakwater during different storm events. These values are compared with the results of the application of state-of-the-art equations for the calculation of pressures on crown walls. The results obtained show the behaviour of the pressures with a crown wall fully protected by the armour, as is the case of Langosteira breakwater. Finally, several conclusions are made on the methodology for measuring the pressures using physical models and the relevance of the armour roughness. Full article
(This article belongs to the Special Issue Coastal Engineering: Sustainability and New Technologies)
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25 pages, 8726 KiB  
Article
Hydraulic Performance of Geotextile Sand Containers for Coastal Defenses
by Sara Corvaro, Carlo Lorenzoni, Alessandro Mancinelli, Francesco Marini and Stefania Rocchi
J. Mar. Sci. Eng. 2022, 10(9), 1321; https://doi.org/10.3390/jmse10091321 - 18 Sep 2022
Cited by 1 | Viewed by 2884
Abstract
Laboratory experiments were performed in the wave flume of the Laboratorio di Idraulica e Costruzioni Marittime of the Università Politecnica delle Marche (Ancona, Italy) to study the hydrodynamic performance of coastal protection structures made of a new type of geotextile sand containers (GSCs). [...] Read more.
Laboratory experiments were performed in the wave flume of the Laboratorio di Idraulica e Costruzioni Marittime of the Università Politecnica delle Marche (Ancona, Italy) to study the hydrodynamic performance of coastal protection structures made of a new type of geotextile sand containers (GSCs). Such structures are used as softer and flexible alternatives to traditional hard coastal defenses made of concrete or rubble mound material. The GSC structures can also be used as temporary coastal protections during the winter period. The physical model reproduced two main configurations: in the former one, the GSCs were used as coastal revetments with three different slopes. In the latter one, the GSCs were applied to make detached submerged breakwaters with different submergences and berm widths. The geometric scale of the models was 1:10, and the weight of each GSC in the prototype was 5 t. The geotextile material of the containers and the wave characteristics were reproduced by using the Reynolds and the Froude similarity criteria, respectively. Reflection coefficients and hydraulic stability behaviors for the revetments, as well as transmission coefficients and piling-up amount for breakwaters, were obtained. Full article
(This article belongs to the Special Issue Non-conventional Coastal Protection Solutions)
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11 pages, 5387 KiB  
Article
Experimental Investigation of the Earth Pressure on Horizontally Composite Breakwaters According to Different Shoulder Widths of Rubble Mounds
by Jae-Sung Lee, Dal Soo Lee and Sang-Ho Oh
Water 2022, 14(14), 2273; https://doi.org/10.3390/w14142273 - 21 Jul 2022
Cited by 1 | Viewed by 2995
Abstract
A series of physical experiments were carried out to investigate the characteristics of the horizontal active earth pressure exerted by rubble stones placed in front of horizontally composite breakwaters. Typically, the shoulder width of rubble mounds is shorter than the failure wedge assumed [...] Read more.
A series of physical experiments were carried out to investigate the characteristics of the horizontal active earth pressure exerted by rubble stones placed in front of horizontally composite breakwaters. Typically, the shoulder width of rubble mounds is shorter than the failure wedge assumed by Rankine’s earth pressure theory; therefore, it is not appropriate to apply the theory for the estimation of the horizontal pressure of rubble stones on the caisson. Considering this, physical experiments were conducted to evaluate the horizontal earth pressure with rubble stones having different shoulder widths in front of the caisson. The experimental results showed that the horizontal pressure was considerably lower than that obtained by Rankine’s theory when the shoulder width was shorter than the failure wedge width. Even when the shoulder width was sufficiently large to apply the theory, the earth pressure was approximately 17% lower than the value calculated byRankine’s theory. Based on these analyses, an empirical equation is proposed that can estimate the earth pressure on the caisson for a wide range of shoulder widths of rubble mounds. Full article
(This article belongs to the Section Oceans and Coastal Zones)
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20 pages, 5320 KiB  
Article
Armor Damage of Overtopped Mound Breakwaters in Depth-Limited Breaking Wave Conditions
by Patricia Mares-Nasarre, Gloria Argente, M. Esther Gómez-Martín and Josep R. Medina
J. Mar. Sci. Eng. 2021, 9(9), 952; https://doi.org/10.3390/jmse9090952 - 1 Sep 2021
Cited by 6 | Viewed by 3594
Abstract
Armor damage due to wave attack is the principal failure mode to be considered when designing conventional mound breakwaters. Armor layers of mound breakwaters are typically designed using formulas in the literature for non-overtopped mound breakwaters in non-breaking wave conditions, although overtopped mound [...] Read more.
Armor damage due to wave attack is the principal failure mode to be considered when designing conventional mound breakwaters. Armor layers of mound breakwaters are typically designed using formulas in the literature for non-overtopped mound breakwaters in non-breaking wave conditions, although overtopped mound breakwaters in the depth-induced breaking wave zone are common design conditions. In this study, 2D physical tests with an armor slope H/V = 3/2 are analyzed in order to better describe the hydraulic stability of overtopped mound breakwaters with double-layer rock, double-layer randomly-place cube and single-layer Cubipod® armors in depth-limited breaking wave conditions. Hydraulic stability formulas are derived for each armor section (front slope, crest and rear slope) and each armor layer. The front slope of overtopped double-layer rock structures is more stable than the front slope of non-overtopped mound breakwaters in breaking wave conditions. When wave attack increases, armor damage appears first on the front slope, later on the crest and, finally, on the rear side. However, once the damage begins on the crest and rear side, the progression is much faster than on the front slope, because more wave energy is dissipated through the armored crest and rear side. Full article
(This article belongs to the Special Issue Breakwater Behaviour)
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