Rubble Mound Breakwaters Research Articles

Numerical Model Study of Prototype Drop Tests on Cube and Cubipod® Concrete Armor Units Using the Combined Finite–Discrete Element Method

This paper aims to evaluate the structural strength of unreinforced concrete armor units (CAU), named Cubipod®, used on rubble-mound breakwaters and coastal structures, through a numerical methodology using the combined finite–discrete element method (FDEM). A numerical modeling methodology is developed to reproduce the results of an experimental examination published by Medina et al. (2011) of a free-fall drop test performed on a 15 t conventional Cubic block and a 16 t Cubipod® unit. The field results of the Cube drop tests were used to calibrate the model. The numerically simulated response to the Cubipod® test is then discussed in the context of a validation study. The calibration process and validation study provide insights into the sensitivity of breakage to tensile strength and collision angle, as well as a better understanding of the crushing and cracking damage of this unit under drop test impact conditions.

Numerical Simulation of Random Wave Overtopping of Rubble Mound Breakwater with Armor Units

Based on the open source code OpenFOAM, a three-dimensional model is presented for simulation of the interaction between waves and rubble mound breakwater with armor units. The armor units with their real geometries are depicted through computational grids. The volume-averaged RANS equation and the seepage equation containing nonlinear term are used to describe the percolation in the core and underlayer of the breakwater. Grids independence analysis are carried out, the horizontal and vertical grid size are recommended to take as one-fifteenth of the mean nominal diameter D50 of the armor units and one-fifteenth of the wave height respectively. Random wave overtopping of rubble mound breakwater with armor units is simulated through the proposed model. The results show good agreement between the simulated and measured overtopping discharge rates for different types of armor units. The developed numerical model can be used to evaluate the random wave overtopping in design of rubble mound breakwater with artificial armor blocs.

Comparison of Existing Equations for the Design of Crown Walls: Application to the Case Study of Ericeira Breakwater (Portugal)

The correct calculation of forces and moments caused by wave action over crown wall structures is critical for their design. There are several existing equations for this, some of which are sanctioned in practice as it is the case for Jensen (1984) and Bradbury et al. (1998), Günback and Gökce (1984), Martin et al. (1999), Berenguer and Baonza (2006), and Pedersen (1996) and Nørgaard et al. (2013). These equations are the main tool for the design of breakwater crown walls and their accuracy is crucial to ensure the stability of the crown wall, especially when considering the sea level rise due to climate change and the possible damage of the armor, since both aspects are not usually considered in most original design studies. In a scenario of climate change, it is very important to estimate the possible changes in security factors due to both these aspects, comparing the results with the original design ones. This paper has as main objective to analyze it for the case study of Ericeira rubble mound breakwater in Portugal. For this, a comparison of the results using those equations and different scenarios including the current, considering sea level rise and armor damage, were performed to extract some conclusions: the increase in the sea level in the case study was not significant and therefore its incidence is very small; and the damage to the main armor by losing pieces at the berm is much more important in this case study, so it is essential to carry out the proper maintenance of the design section. On the other hand, horizontal forces are more conservative using Pedersen and Nørgaard equations, obtaining the lowest value with Martin. Regarding uplift pressures, Martin gives the lowest value, while the most conservative values are given by Günbak and Gökce’s for two scenarios, and Pedersen and Nørgaard for the other two scenarios. Furthermore, the sliding safety coefficient is more conditioning than overturning the safety coefficient in all the scenarios.

Wave RUN-UP Measurements under very oblique wave incidence

Under the scope of the HYDRALAB+ transnational access project, the so-called RODBreak experiment was conducted in the multidirectional wave basin at the Marienwerden facilities of the Leibniz University Hannover (LUH). A stretch of a rubble-mound breakwater was built in the wave basin with a very gentle slope. Its armour layer was made of Antifer cubes, at the roundhead and adjoining trunk, and of rock, at the rest of the trunk. A set of tests was carried out to extend the range of wave steepness values analysed in wave run-up, overtopping and armour layer stability studies, focusing on oblique extreme wave conditions, with incident wave angles from 40º to 90º. The present study focuses on the analysis of measured wave run-up values obtained in the tests and on their on their variability as well as the influence of the wave obliquity and directional spreading. Keywords: rubble-mound breakwaters; run-up; oblique waves; physical modelling; RODbreak.

Design of rubble mound slope protection for cellular cofferdam breakwater retrofitting

A rubble mound slope structure was designed to protect a decaying cellular steel sheet pile cofferdam breakwater which has been partially damaged. Reparation of this decaying cofferdam breakwater to its original form is considered uneconomic. Considering three basic design requirement, i.e. economic feasibility, environmental sustainability, and structural reliability and constructability, the rubble mound slope design has been proposed as a retrofit structure against 4.7m height of a 100yrs return period design wave. In this design, the existing vertical cofferdam stands originally at the harbour side, whereas the new additional rubble mound structure is attached to the cofferdam at the sea side creating together a new horizontal composite breakwater. The existing cofferdam supports the rubble mound structure at the harbour side, whereas the rubble mound structure provides protection against direct wave attack. This retrofit design of structure requires less 25% of materials volume and costs 30% cheaper than a full standalone rubble mound breakwater type. This less requirement of materials will consequently have positive impact on environment and natural resource conservation. The design of rubble mound slope that is directly attached to the existing breakwater will enable its easy construction by using vehicles that stand on the top of the existing breakwater. This article describes the design consideration including discussion on the structural reliability of the retrofitted breakwater.

Level III Reliability Design of an Armor Block of Rubble Mound Breakwater Using Probabilistic Model of Wave Height Optimized for the Korean Sea Wave Conditions and Non-Gaussian Wave Slope Distribution

In this study, a Level III reliability design of an armor block of rubble mound breakwater was developed using the optimized probabilistic wave height model for the Korean marine environment and Van der Meer equation. To demonstrate what distinguishes this study from the others, numerical simulation was first carried out, assuming that wave slope follows Gaussian distribution recommended by PIANC. Numerical results showed that Gaussian wave slope distribution overpredicted the failure probability of armor block, longer and shorter waves, and on the contrary, underpredicted waves of the medium period. After noting the limitations of Gaussian distribution, some efforts were made to develop an alternative for Gaussian distribution. As a result, non-Gaussian wave slope distribution was analytically derived from the joint distribution of wave amplitude and period by Longuet–Higgins using the random variables transformation technique. Numerical results showed that non-Gaussian distribution could effectively address the limitations of Gaussian distribution due to its capability to account for the nonlinear resonant wave–wave interaction and its effects on the wave slope distribution that significantly influences the armor block’s stability. Therefore, the non-Gaussian wave slope distribution presented in this study could play an indispensable role in addressing controversial issues such as whether or not enormous armor blocks like a Tetrapod of 100 t frequently mentioned in developing countermeasures against rough seas due to climate change is too conservatively designed.

Large Deformation Finite Element Modeling of Rubble Mound Breakwater Built on Soft Seabed Using Coupled Eulerian–Lagrangian Method

For the design of rubble mound breakwaters on soft soil, it is essential to predict the behavior of soft soil and large deformations phenomena occurring in the course of construction of the rubble mound breakwater. Large deformations in various problems can be well simulated using the coupled Eulerian–Lagrangian (CEL) method. In this study, the CEL method has been used to simulate the rubble mounds construction on soft soil and predict the resulting settlements. To validate the numerical model, the results of three experiments conducted in the physical modeling laboratory at Kharazmi University were used. Also, two case studies of real rubble mound breakwaters constructed on soft seabeds were numerically simulated and the results of the numerical model were compared with the recorded data. According to the obtained results, the finite element analysis by the CEL method is able to predict the deformations and settlement occurred during construction of rubble mound breakwaters on soft soils with a reasonable accuracy. In very soft soils with undrained shear strength less than 10 kPa, the CEL simulation outperformed the Lagrangian formulation. Then, parametric study was performed and the effects of height, crest width, breakwater slope and thickness and strength of the soft soil on the amount of rubble mound settlement were investigated.

Time dependent investigation of the wave induced scour at the trunk section of a rubble mound breakwater

Rubble-mound breakwaters are the most commonly constructed marine structures for various port structures with different areas of usage. Local scour around these structures, which leads to stability losses or even failure, has great importance for the design of these structures both economical and safety perspectives. Within the scope of this paper, wave-induced local scour at the toe of rubble mound breakwaters placed on an erodible seabed was studied both experimentally and numerically. Experiments were carried out on the wave channel in Hydraulics Laboratory of Dokuz Eylul University. Time dependent scour depth and wave characteristics were observed with ultrasonic methods. An equivalent numerical wave channel was used to compare and observe scour mechanism. Regular waves were generated by using Flow3D, one of the advanced computational fluid dynamics (CFD) software. Scour patterns were investigated for relatively coarse and fine seabed material with 1.85 mm and 0.55 mm grain median diameters under various wave scenarios with a breakwater slope of 1:1.5 and 1:1.75 which are widely used in construction. From the experimental and numerical findings obtained from the study, it is understood that the numerical model was found to be compatible with experiments.

Boundary element method for wave trapping by a multi-layered trapezoidal breakwater near a sloping rigid wall

This study examines the multiple layers in a rubble mound breakwater and their effect on reflection and dissipation of incoming ocean waves. The numerical model is developed using multi-domain boundary element method for oblique water wave trapping near a sloping wall by a multi-layered trapezoidal porous structure, which is utilized to model armour, filter and core layers while examining the hydrodynamics in different configurations. Both, the constant element and linear element approaches to boundary element method are discussed. The cases of bottom-standing porous structures as being submerged and fully extended are considered. The wave hydrodynamics over the structure is described by the reflection and dissipation coefficients along with the forces acting on the sloping wall, and is influenced by wave and structural parametrics of the system. The influence of armour layer in different configurations is highlighted for various structural and wave parameters.

Numerical Investigation on Hydrodynamic Energy Conversion Performance of Breakwater-Integrated Oscillating Water Column-Wave Energy Converters

Various wave energy converters (WECs) have been developed to utilize ocean wave energy resources. Among them, an oscillating water column (OWC) device is a promising wave energy converter that has undergone several pilot tests in the ocean with various prototype devices. Recently, a breakwater-integrated OWC-WEC system was proposed to improve the economic feasibility by reducing the construction and installation costs of the OWC chamber structure. In this study, a numerical investigation was conducted to simulate the hydrodynamic energy conversion problem for a breakwater-integrated OWC-WEC. The boundary value problem with the Laplace equation was solved directly by using a three-dimensional numerical wave tank based on a finite element method in the time domain. In the present numerical method, an efficient numerical model for the tetrapod (TTP), which is an armored rubble mound breakwater, was introduced using multiple blocks and numerical damping zone. Further, numerical investigations were performed on the effects of breakwater integration, TTP layer modeling, and the application of the numerical damping zone, and their features in terms of the wavefield and the OWC chamber responses were analyzed. Finally, the validity of the present numerical method was examined by comparing it with the experimental data.

STUDY OF RAPID SEDIMENTATION AT PARESAR INTAKE BASIN, CASPIAN SEA, DUE TO LARGE WRACK PARTICLES AND WIND-INDUCED CURRENTS

The rapid sedimentation at the entrance of Paresar intake basin is studied, in which unnatural wrack accumulation at the coast, combined with the existing sand, resulted in a major increase in the actual Longshore Sediment Transport (LST) rate. Considering the volume of updrift fillet at the northwest of main breakwater and the estimated LST rate, the advancement of updrift shoreline was highly unexpected. Sands and vegetative wracks were observed only 3 years after constructing the rubble mound breakwaters, resulting in water depth decrease at the entrance. Employing field measurements and numerical modeling, it is revealed that general wind-induced currents in Caspian Sea, which were ignored in the design, have a small effect on increasing LST rate. The unusual sedimentation can be mainly related to the high percentage of wrack particles at updrift coast.Recorded Presentation from the vICCE (YouTube Link): https://youtu.be/UNNnjDHL41k

ROUGHNESS FACTOR FOR MULTI-LAYER ARMOUR AS OVERTOPPING ESTIMATOR

Nowadays one of the most challenging problem for engineers is to adapt existing coastal structures to climate changes. Wave overtopping is highly sensitive to the increasing extreme water depths due to higher storm surges coupled with sea level rise. One way to face these problems for rubble mound breakwaters is to add one or more layers to the existing armour. Prediction of wave overtopping of coastal structures is presently obtained from empirical formulae in EurOtop (2018). For the case of overtopping over multi-layer armour, no validated method exists, so prediction must be based upon assumptions and judgement, with related uncertainties. This study is focused on the effects of different types of armour, the number of layer and other structural characteristics on the roughness factor f. The main effects of porosity and roughness will be investigated. This paper analyzes the results of several new physical model tests of different rubble mound breakwaters reproduced at the new medium scale random wave flume of the Department of Engineering of Roma Tre University.Recorded Presentation from the vICCE (YouTube Link): https://youtu.be/8cOdqkqQ-9s

MODELLING OF WAVE OVERTOPPING LOADS ON A BUILDING BEHIND A RUBBLE MOUND BREAKWATER USING A 2DV NUMERICAL MODEL AND THEIR APPLICATION IN BUILDING DESIGN

This study considers the wave overtopping loads on a building behind a rubble mound breakwater using 2D numerical modelling. The building will be used as Coast Guard station in Greystones Marina, which is located on the Irish Sea. Similar studies, using physical modelling, were carried out recently by Watson et al. (2018) and Park et al. (2017). The applicability of the numerical model in predicting wave overtopping forces is discussed. Appropriate design wave conditions are considered and the resultant loads are assessed to determine their impact on the design of the proposed building.Recorded Presentation from the vICCE (YouTube Link): https://youtu.be/4tZfjVDRPT4

STABILITY OF HIGH DENSITY CUBES IN RUBBLE MOUND BREAKWATERS

The stability number for rubble mound breakwaters is a function of several parameters and depends on unit shape, placing method, slope angle, relative density, etc. In this study two different densities for cubes in breakwater armour layers were tested to determine the influence of the density on the stability. The experimental results show that the stability of high density blocks were found to be more stable and the damage initiation for high density blocks started at higher stability numbers compared to normal density cubes.

A NEW REDUCTIVE FACTOR FOR THE WAVE OVERTOPPING DISCHARGE AT CROWN WALLS BASED ON GENETIC PROGRAMMING

The upgrade of existing coastal defense structures by including crown walls and parapets may represent an effective and economic solution to reduce the wave overtopping discharge. Recently, a coefficient gs_GP for the parametrization of the effects induced by berms or promenades, crown walls and parapets on the average q has been developed. The formula for gs_GP was obtained from the Genetic Programming (GP) technique and was conceived to be included in the q formulae by EurOtop Manual (2018). The formula has been applied so far only to smooth dikes with crown walls. The aim of this contribution is to investigate the extension of the formula for gs_GP to a wider range of coastal structures, such as crown walls on top of rubble mound breakwaters and vertical seawalls. The ultimate objective is to provide a new design factor to be used in the EurOtop formulae.Recorded Presentation from the vICCE (YouTube Link): https://youtu.be/2xWPJeXPRco

Subsidence prediction of a rubble mound breakwater at Yantai port: A application of FSSI-CAS 2D

This study is an application of the integrated numerical model FSSI-CAS 2D, to predict the subsidence of a huge rubble mound breakwater in the west part zone at Yantai port. The modified Cambridge clay soil model and poro-elastic model are adopted to describe the quasi-static mechanical behavior of the seabed foundation, which is consists of muddy-clay, clay and silt soil layers. The model parameters of soil used in computation are estimated based on a great number of laboratory tests (over one thousand). A novel point is that the buoyancy applied on the rubble mounds under SWL (Static Water Line), as well as its nonlinear variation dependent on the deformation of seabed foundation are considered in computation. Through analytical and experimental verification, as well as the comparison with observation data monitored in-situ, it is indicated that FSSI-CAS 2D is reliable to numerically predict the subsidence of offshore structures, and has the ability to be applied in practical engineering.

Experimental Study of Rubble Mound Behavior on the Very Soft Soil Seabed

The construction of rubble mound structures such as a breakwater or access road on a very soft seabed is essential to the development of maritime transportation. This process can result in significant settlement that causes the rock particles to sink into the seabed, leading to loss of material. In the current study, several case studies on breakwaters facing large settlements, which resulted in the use of excessive amounts of rubble, were surveyed. A series of physical models were developed to study the deformation and volume loss of rubble mound breakwaters on very soft clayey soil during construction. It was found that most deformation occurred early in construction. The primary mechanisms influencing settlement were rock penetration into the soft bed, flow of clay material into the porous body of the rubble mound, and lateral deformation of the soil beneath the breakwater, which is associated with soft bed heave at the breakwater toe. During testing of very soft beds, the ratio of material loss to the design weight of the rubble mound increased up to 27%, and the proportion of penetration to total material loss was as high as 56%. The results of the experiments and case studies were used to develop an empirical relation with which to predict settlement.

Composite breakwater of a submerged horizontal flexible porous membrane with a lower rubble mound

An analytical solution of a new composite breakwater consisting of a moored submerged flexible porous membrane and a submerged ruble mound below the membrane is presented. The semi-analytical solution is obtained based on the velocity potential decompositions where the consideration of a dispersion relation with complex wave numbers is not required. The convergence of the series solution is demonstrated by computing the values of the reflection, the transmission, the dissipation coefficients and the vertical force. In addition, the present results are compared against published numerical results and experimental data. In order to analyze the efficiency of the newly developed composite breakwater, the present results are compared with those of a single horizontal submerged moored porous membrane and a single rubble mound breakwater. Furthermore, the effects of design parameters on the performance of the composite breakwater are also analyzed in detail.

Effect of basal reinforcement on sinking and deformation of rubble mounds on a soft seabed

ABSTRACT The construction of rubble-mound breakwaters on soft sea beds is problematic, but is necessary in many coastal areas. The issues faced include the penetration of the rock particles into the very soft clayey bed, which results in the loss some of the material, major deformation during and after construction, and instability. The basal reinforcement method employs both separation and reinforcement and is an effective solution. Most previous research has focused on the role of reinforcement, but less attention has been paid to the combination of reinforcement and separation. In the present study, physical model tests were used to quantitatively compare the action mechanisms of the basal reinforcement method and the gravity replacement method. The experimental results showed that the use of a geotextile for basal reinforcement reduced horizontal deformation up to 42%, but had no significant effect on settlement. The combined reinforcement and separation mechanisms also reduced material loss up to 44%.

Evaluation of the annual electricity production of a hybrid breakwater-integrated wave energy converter

Ocean waves constitute an abundant source of clean and predictable energy, with the potential to partly replace carbon intensive energy sources. At present, several technologies to convert wave energy into electricity are being developed, but those suitable for integration into port breakwaters present additional advantages. This paper presents a novel concept that combines two well-known wave energy conversion principles, an oscillating water column and a multi-reservoir overtopping system. This hybrid concept was designed to be integrated in rubble-mound breakwaters, having as case study Leixões’ northern breakwater, Portugal. The performance and efficiency of the single components were assessed separately as well as that of the hybrid module as a whole, to demonstrate the advantages of their combination into a single unit. Furthermore, the annual energy production was estimated for a 20 m wide hybrid module considering the local metocean conditions. Results showed that overall efficiency amounted to circa 44.4%, the wave-to-wire efficiency to 27.3% and the annual electricity production was estimated at 35 MWh/m. Considering that 240 m of the reference breakwater are used, the developed hybrid module could provide approximately 50% of the electricity consumption of the Port of Leixões, which demonstrates the potential and interest of the developed technology.