Perforated Caisson Breakwater Research Articles

Numerical simulation on hydrodynamic performance of perforated caisson breakwater with slotted shoreward wall

The purpose of this study is to investigate wave reflection and overtopping of perforated caisson breakwater with a slotted shoreward wall (PCB–S) under regular wave conditions. A numerical wave tank, solving the two-dimensional Reynolds-averaged Navier-Stokes equations with the k-ω turbulence closure and employing the VOF model for free surface capturing, is validated against experiments. The study thoroughly explores the influence of various factors, such as wave steepness, front wall porosity, relative wave chamber width, submergence depth of the shoreward wall slot, and shoreward wall porosity, on the reflection coefficient, wave overtopping discharge, and exit flow velocity. The distribution of vorticity and turbulent kinetic energy around PCB-S were clarified to better understand wave dissipation mechanism. The results show that the PCB-S improves the water exchange between the inside and behind the caisson and effectively reduces the reflection coefficient and the overtopping discharge. The simulation results pointed out that the relative wave chamber width B/L = 0.1, the relative submergence depth of the slot s/d = 0.33–0.42, and the porosity of the shoreward wall ε2 = 0.1–0.12 are most conducive to the reduction of the reflection coefficient of the waves.

Comparative study on semi-probabilistic design methods to calibrate load and resistance factors for sliding stability design of caisson breakwaters

The partial safety factor method commonly necessitates a set of multiplying factors (MFs) to modify the basic variables; hence, when multiple variables are included, it is complicated for design practice. Conversely, the load and resistance factor design (LRFD) format is more practical since it utilizes fewer factors to adjust loads and resistance. This study carries out a comparative study of the two semi-probabilistic design formats and four calibration methods to determine the more suitable design approach and establish associated factors for sliding stability designs of caisson breakwaters under wave and seismic conditions. To fulfill the aforementioned purposes, 12 perforated caisson breakwaters are first selected; thereafter, four calibration methods, which include a closed-form solution and three scenarios based on Monte Carlo simulation (MCS), are executed to determine individual MFs for each case. The final single set of MFs for design practice is calibrated via an optimization process. The present study shows that the two design formats can provide similar solutions. Hence, the LRFD-based concept is recommended to be applied owing to its easier implementation in code calibrations and design practices. Moreover, the performance of the shifting-technique-MCS-based calibration (the simplest simulation) is thoroughly investigated, and it is then found that this approach must be used with care if the target safety considerably varies from the initial safety level. In the present work, an efficient and accurate approximation method to specify the final MFs set is proposed because the optimization-based calibrations to determine the final set of MFs are time-consuming and expensive to evaluate.

Experimental and numerical studies of solitary wave interaction with perforated caisson breakwaters

This study experimentally and numerically investigated interactions between solitary waves and the perforated caisson breakwaters. By caisson, we mean a sealed chamber filled with sand and rocks inside, and it is a common structure used for the construction of vertical breakwater. In the laboratory, the solitary waves with larger relative wave heights were well generated based on the “collapsing water column” technique and successfully acted on the perforated caisson models. Using the volume of fluid method and the k–ε model, combined with the ideal gas equation at a constant temperature, the wave transformation and vortex evolution in the vicinity of the perforated caisson breakwaters were simulated. A reasonable agreement was observed between the numerical and the experimental results. By comparing with the non-perforated caissons, the perforated caissons effectively reduced the reflected and transmitted wave heights, and the occurrence of the reflected waves was found to be delayed due to the existence of the wave chamber. Based on the numerical results, distributions of the fluid velocity and turbulence kinetic energy (TKE) near the perforated caissons were examined. The wave dissipation mechanism of perforated caisson under the solitary wave was different from that under the periodic wave. The results showed that vortices and TKE were mainly concentrated near the perforated front wall. The incident wave energy was dissipated in the generating vortices formed by fluids jetting through perforations. Additionally, variations of the wave reflection, transmission, dissipation coefficients, and wave overtopping volumes were investigated against different relative crest freeboards, relative wave chamber widths, caisson porosities, and relative wave heights under the solitary waves. Valuable results were presented for practical engineering applications.

Experimental Study of Irregular Wave Reflection by a Perforated Caisson Breakwater Under Wave Overtopping Conditions

Experimental Study of Irregular Wave Reflection by a Perforated Caisson Breakwater Under Wave Overtopping Conditions

Breaking wave impact on perforated caisson breakwaters: A numerical investigation

With the use of a pressure-based compressible flow solver, the issue of breaking wave impact on perforated caisson breakwaters (PCBs) is comprehensively investigated. The wave profile at the moment of impact, the pressure induced by breaking waves, and the wave−structure interaction process, are detailed. Three key findings are concluded: (i) air is inevitably trapped in the impact process because the water inside the wave absorption chamber (WAC) leaks through the perforated wall and then drops into the water in front of the PCB, causing water aeration; (ii) the upward pressure inside the opening above the still water level is close or even greater than the pressure on the perforated wall, and this upward pressure might be directly scaled as per the Froude law because no air is trapped; (iii) most of the commonly used empirical formulae fail to provide a reasonable prediction of the maximum pressure and force on the PCB induced by breaking waves. Finally, a comparatively large wall porosity, such as 0.4, is recommended in the design of PCBs because it is beneficial to diminishing the maximum pressure on the perforated wall and inside the opening, as well as the maximum horizontal force on the PCB.

Calibration of Load and Resistance Factors for Breakwater Foundation Design. Application on Different Types of Superstructures

Load and resistance factor design is an efficient design approach that provides a system of consistent design solutions. This study aims to determine the load and resistance factors needed for the design of breakwater foundations within a probabilistic framework. In the study, four typical types of Korean breakwaters, namely, rubble mound breakwaters, vertical composite caisson breakwaters, perforated caisson breakwaters, and horizontal composite breakwaters, are investigated. The bearing capacity of breakwater foundations under wave loading conditions is thoroughly examined. Two levels of the target reliability index (RI) of 2.5 and 3.0 are selected to implement the load and resistance factors calibration using Monte Carlo simulations with 100,000 cycles. The normalized resistance factors are found to be lower for the higher target RI as expected. Their ranges are from 0.668 to 0.687 for the target RI of 2.5 and from 0.576 to 0.634 for the target RI of 3.0.

Analysis of oblique wave interaction with perforated caisson breakwaters with partial wave absorption parts

This article presents a three-dimensional (3D) iterative analytical solution for water wave interactions with perforated caisson breakwaters with partial wave absorption parts based on linear potential flow theory. A periodic boundary condition is adopted for developing the series solutions of the velocity potentials by the separation of variables method. A quadratic pressure drop condition is imposed on the perforated walls to introduce wave energy dissipation. The unknown expansion coefficients in the velocity potentials are determined by matching the boundary conditions between adjacent fluid domains combined with iterative calculations. The hydrodynamic quantities, including the reflection coefficient, wave forces, and free surface elevation, are estimated. The convergences of the series solutions and the iterative calculation process are examined. The analytical solution calculations agree well with the known analytical and experimental results for special cases in the literature. Variations in the hydrodynamic quantities versus the main influencing factors are clarified. Partial wave absorption concept design enables the hydrodynamic performance of the present caisson breakwater with a smaller perforated wall area to be similar to that of a fully perforated caisson breakwater. To achieve a lower reflection coefficient and wave forces, the ratio of the wave chamber length to the caisson length is suggested to be 0.3–0.5, and the front wave chamber width should be less than half of the total wave chamber width.

Experimental Study on Hydraulic Performance of Tiecell Caisson Breakwater with Wave Chamber

Kim, I.-C.; Park, K., and Kang, T.-W., 2021. Experimental study on hydraulic performance of tiecell caisson breakwater with wave chamber. In: Lee, J.L.; Suh, K.-S.; Lee, B.; Shin, S., and Lee, J. (eds.), Crisis and Integrated Management for Coastal and Marine Safety. Journal of Coastal Research, Special Issue No. 114, pp. 81–85. Coconut Creek (Florida), ISSN 0749-0208. Recently, a perforated caisson breakwater with tiecell blocks was developed to improve a water affinity and people's safety of a rubble mound armoured by tetrapods. In this study, hydraulic model tests were performed to examine the hydraulic performance of a non-porous and a tiecell caissons with perforated blocks attacking wave against a small fishery harbor near Busan. The model test results show that the tiecell caisson is more effective in dissipating wave energy under normal wave conditions and in reducing wave overtopping rates under design wave conditions than the non-porous caisson. It is found that the horizontal wave forces acting on the tiecell caisson show slightly more large than the non-porous caisson due to the impulsive force generated in the wave chamber.

Numerical investigation into effect of the rubble mound inside perforated caisson breakwaters under random sea states

The paper reports a numerical investigation into the effect of rubble mounds inside perforated caisson breakwaters (PCBs), in which a line-shaped mass source wavemaker is proposed for generating random waves. A series of experiments are employed to validate the numerical model, and good agreements are observed in the comparison of the experimental and numerical results. With the use of the validated numerical model, the numerical investigation is performed, in which the attention is mainly paid to two parameters: the slope angle and porosity of the inner rubble mound. The result shows that, as the slope angle of the inner rubble mound increases, the reflection coefficient is observed to decrease first and then increase, and compared to the experiment, both the positive and negative hydrodynamic pressure acting on the solid rear wall of PCBs is weakened. On the other hand, although a larger inner rubble mound porosity is beneficial to diminish the reflection coefficient, the reduction is not obvious especially when the front wall porosity is small. Furthermore, as the increase of front wall porosity and relative wave absorption chamber length (the ratio of wave absorption chamber length to significant wavelength), the effect of the slope angle and porosity of the inner rubble mound becomes more significant because more waves could enter the wave absorption chamber. The relative wave absorption chamber length considered in the present study ranges from 0.06 to 0.21, and the recommended slope angle is approximately 45 degrees.

Calibration of Load and Resistance Factors for Breakwater Foundations under the Earthquake Loading

This study investigates the system stability of breakwater foundations subjected to earthquakes from a probabilistic point of view. A fully probabilistic approach, i.e., a combination of the Monte Carlo simulation and Bishop’s simplified method, has been developed to evaluate the system failure probability of foundation damage, one of the prevailing failures encountered during earthquakes. Twelve sections of perforated caisson breakwaters located around Korea were chosen as case studies. First, the reliability analysis was performed for all the breakwaters at existing conditions; then, the calibration process involving the estimation of load and resistance factors was conducted for 12 breakwaters at three levels of the target reliability index. As the performance function, used in the stability analysis of breakwater foundations, is defined based on an implicit shape with a high-dimensional space of variables, the calibration process of load and resistance factors becomes cumbersome and complicated. Therefore, this study has proposed a sensitivity analysis to be implemented prior to the calibration process to elicit the effects of variables on the stability of each breakwater, which, thereafter, effectively directs the calibration process. The results of this study indicate that the failures in the foundation of breakwaters frequently occur in different modes. Therefore, the failure probability should be estimated considering all possible failure modes of the foundation. The sensitivity results elucidate that the soil strength parameters are the dominant variables, contributing to the stability of foundations, whereas the seismic coefficient presents the negative effect, causing the insecurity of breakwaters. In particular, the deadweights, though directly contributing to the seismic forces, show a small effect on the stability of foundations. The calibration shows that the load factors slightly vary with an increase in the target reliability index and set 1.10 for three safety levels. In contrast, the resistance factor exhibits an inverse relationship with the specified reliability index. Especially when the load factor equals 1.10, the resistance factors are 0.90, 0.85, and 0.80, corresponding to the reliability index of 2.0, 2.5, and 3.0, respectively. Eventually, it is proved that the sensitivity analysis prior to the calibration process makes the procedure more efficient. Accordingly, the iteration of simulation execution is diminished, and the convergence is quickly accomplished.

Load & Resistance Factors Calibration for Sliding and Overturning Limit State Design of Perforated Caisson Breakwater

Load & Resistance Factors Calibration for Sliding and Overturning Limit State Design of Perforated Caisson Breakwater

Numerical simulation of wave overtopping above perforated caisson breakwaters

A two-dimensional numerical model was used to study the wave overtopping performance above perforated caisson breakwaters under regular waves. The turbulent flow was simulated by solving the Reynolds Averaged Navier–Stokes (RANS) equations and the k–ε turbulence model equations. In the numerical wave flume, the free surface was tracked by the Volume of Fluid (VOF) method, and a relaxation zone was added to avoid the unwanted re-reflection from the inflow boundary. Based on the ideal gas equation at a constant temperature, the pressure change caused by the compressed air inside the wave chamber was incorporated into the numerical model for accurately simulating the wave motion inside the wave chamber. The numerical results of the free surface elevations inside and outside the wave chamber, the wave overtopping discharges and the reflection coefficients of perforated caisson breakwaters were in good agreement with the experimental data. This means that the numerical model is valid in estimating wave action and overtopping on complicated coastal structures with perforated thin walls. The distributions of flow velocity and turbulence kinetic energy (TKE) around the perforated caissons were clarified, which gave a better understanding of the wave overtopping mechanism above the perforated caisson breakwaters. Numerical results showed that the wave energy transferred by the overtopping flows is much smaller than that dissipated by the perforated caisson breakwater. When the relative freeboard (the ratio of the crest freeboard to the incident wave height) of the perforated caisson breakwater was larger than 0.58, the existence of the overtopping flow has no significant influence on the reflection coefficient. Besides, avoiding the air compression inside the wave chamber can effectively reduce the overtopping discharge. Increasing the caisson porosity or the wave chamber width can also reduce the overtopping discharge above the perforated caisson breakwaters.

Iterative analytical solution for wave reflection by a multi-chamber partially perforated caisson breakwater

This study examines wave reflection by a multi-chamber partially perforated caisson breakwater based on potential theory. A quadratic pressure drop boundary condition at perforated walls is adopted, which can well consider the effect of wave height on the wave dissipation by perforated walls. The matched eigenfunction expansions with iterative calculations are applied to develop an analytical solution for the present problem. The convergences of both the iterative calculations and the series solution itself are confirmed to be satisfactory. The calculation results of the present analytical solution are in excellent agreement with the numerical results of a multi-domain boundary element solution. Also, the predictions by the present solution are in reasonable agreement with experimental data in literature. Major factors that affect the reflection coefficient of the perforated caisson breakwater are examined by calculation examples. The analysis results show that the multi-chamber perforated caisson breakwater has a better wave energy dissipation function (lower reflection coefficient) than the single-chamber type over a broad range of wave frequency and may perform better if the perforated walls have larger porosities. When the porosities of the perforated walls decrease along the incident wave direction, the perforated caisson breakwater can achieve a lower reflection coefficient. The present analytical solution is simple and reliable, and it can be used as an efficient tool for analyzing the hydrodynamic performance of perforated breakwaters in preliminary engineering design.

Corrigendum to: Experimental Study on Hydraulic Performance of Perforated Caisson Breakwater with Turning Wave Blocks

Corrigendum to: Experimental Study on Hydraulic Performance of Perforated Caisson Breakwater with Turning Wave Blocks

Interaction analysis between waves and perforated caisson using the revised smoothed particle hydrodynamics method and finite element method

A two-dimensional smoothed particle hydrodynamics analysis model based on Riemann solution is put forward to discuss its application for the wave-perforated caisson interaction problem. The wave particles are simulated by the smoothed particle hydrodynamics method and the perforated caisson employs the finite element method. The numerical method has been verified by comparing the process of elastic plate with liquid tank with test, and a good agreement is reached. Then, the proposed method is employed to study the distribution of dynamic stress in the perforated plate position of dissipation chamber at the still water level, as well as the distribution of dynamic stress along the perforated plate. Furthermore, the relationship between the dynamic stress and the corresponding coefficient is also discussed, such as the relative width B/L of dissipation chamber of no-roof perforated caisson and the relative height s/L of top cover of perforated caisson. This article concludes by providing reference to the design and construction of perforated caisson breakwaters.

Experimental Study on Hydraulic Performance of Perforated Caisson Breakwater with Turning Wave Blocks

Experimental Study on Hydraulic Performance of Perforated Caisson Breakwater with Turning Wave Blocks

WAVE PRESSURE FORMULA FOR PERFORATED CAISSON WITH DOUBLE CHAMBERS

Some of perforated caisson breakwaters have double wave chambers, for which no clear guideline for estimating design load is available. The well-known Takahashi's formula (Takahashi and Shimosako, 1994) is basically applicable to single-chamber perforated caisson. Considering this, we conducted physical experiment to develop a wave pressure formula for double-chamber perforated caisson.

Experimental study of mean overtopping discharge at perforated caissons for non-impulsive waves

In this study, hydraulic model tests are carried out to investigate the mean overtopping discharge at perforated caisson breakwaters for non-impulsive waves. Based on the experimental data, the mean overtopping discharges of perforated and non-perforated caissons are compared. It is found that when the relative crest freeboard is smaller than 1.6, the mean overtopping discharge of a breakwater can be reduced by at least half by using perforated caissons with 35% porosity instead of non-perforated caissons. The effects of the relative crest freeboard, the caisson porosity and perforation shape, the relative wave chamber width and the relative water depth on the mean overtopping discharge at perforated caissons are clarified. Then, predictive formulas for the mean overtopping discharge at perforated caissons are developed. The predictive formulas based on the experimental data are valid in a wide range of the relative crest freeboard and involve the effects of the caisson porosity and the relative water depth. The predictive formulas developed in this study are of significance for the hydraulic design of perforated caissons.

Three-dimensional Simulation of Wave Reflection and Pressure Acting on Circular Perforated Caisson Breakwater by OLAFOAM

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Iterative multi-domain BEM solution for water wave reflection by perforated caisson breakwaters

This study develops a full solution for water wave reflection by a partially perforated caisson breakwater with a rubble mound foundation using multi-domain BEM (boundary element method). Regular and irregular waves are both considered. A quadratic pressure drop condition on caisson perforated wall is adopted, and direct iterative calculations are performed. Due to the use of quadratic pressure drop condition, the effect of wave height on the energy dissipation by the perforated wall is well considered. This study also develops an iterative analytical solution for wave reflection by a partially perforated caisson breakwater on flat bottom using matched eigenfunction expansion method. The reflection coefficients calculated by the multi-domain BEM solution and the analytical solution are in excellent agreement. The present calculated results also agree reasonably well with experimental data from different literatures. Suitable values of discharge coefficient and blockage coefficient in the quadratic pressure drop condition are recommended for perforated caissons. The effects of the wave steepness, the blockage coefficient of perforated wall and the relative wave chamber width on the reflection coefficient are clarified. The present BEM solution is simple and reliable. It may be used for predicting the reflection coefficients of perforated caisson breakwaters in preliminary engineering design.