This study examines the hydrodynamic performance of multiple-row vertical slotted breakwaters. We developed a mathematical model based on an eigenfunction expansion method and a least squares technique for Stokes seco...This study examines the hydrodynamic performance of multiple-row vertical slotted breakwaters. We developed a mathematical model based on an eigenfunction expansion method and a least squares technique for Stokes second-order waves. The numerical results obtained for limiting cases of double-row and triple-row walls are in good agreement with results of previous studies and experimental results. Comparisons with experimental measurements of the reflection, transmission, and dissipation coefficients （CR, Cr, and CE） for double-row walls show that the proposed mathematical model adequately reproduces most of the important features. We found that for double-row walls, the CR increases with increasing wave number, kd, and with a decreasing permeable wall part, din. The Cr follows the opposite trend. The CE slowly increases with an increasing kd for lower kd values, reaches a maximum, and then decreases again. In addition, an increasing porosity of dm would significantly decrease the CR while increasing the Cr. At lower values of kd, a decreasing porosity increases the CE, but for high values of kd, a decreasing porosity reduces the Ce. The numerical results indicate that, for triple-row walls, the effect of the arrangement of the chamber widths on hydrodynamic characteristics is not significant, except when kd〈0.5 Double-row slotted breakwaters may exhibit a good wave-absorbing performance at kd〉0.5, where by the horizontal wave force may be smaller than that of a single wall. On the other hand, the difference between double-row and triple-row vertical slotted breakwaters is marginal.展开更多
The reliability of a vertical breakwater is calculated using direct integration methods based on joint density functions.The horizontal and uplifting wave forces on the vertical breakwater can be well fitted by the lo...The reliability of a vertical breakwater is calculated using direct integration methods based on joint density functions.The horizontal and uplifting wave forces on the vertical breakwater can be well fitted by the lognormal and the Gumbel distributions,respectively.The joint distribution of the horizontal and uplifting wave forces is analyzed using different probabilistic distributions,including the bivariate logistic Gumbel distribution,the bivariate lognormal distribution,and three bivariate Archimedean copulas functions constructed with different marginal distributions simultaneously.We use the fully nested copulas to construct multivariate distributions taking into account related variables.Different goodness fitting tests are carried out to determine the best bivariate copula model for wave forces on a vertical breakwater.We show that a bivariate model constructed by Frank copula gives the best reliability analysis,using marginal distributions of Gumbel and lognormal to account for uplifting pressure and horizontal wave force on a vertical breakwater,respectively.The results show that failure probability of the vertical breakwater calculated by multivariate density function is comparable to those by the Joint Committee on Structural Safety methods.As copulas are suitable for constructing a bivariate or multivariate joint distribution,they have great potential in reliability analysis for other coastal structures.展开更多
The Oscillating Water Column(OWC) wave energy convertor with the advantage of its simple geometrical construction and excellent stability is widely employed.Recently,perforated breakwaters have been often used as they...The Oscillating Water Column(OWC) wave energy convertor with the advantage of its simple geometrical construction and excellent stability is widely employed.Recently,perforated breakwaters have been often used as they can effectively reduce the wave reflection from and wave forces acting on the structures.Considering the similarity between the compartment of perforated caisson and the air chamber of OWC wave energy convertor,a new perforated caisson of breakwater is designed in this paper.The ordinary caisson is modified by installing facilities similar to the air chamber of OWC converter,but here they are utilized to dissipate the wave energy inside the caisson.Such an arrangement improves the stability of the caisson and reduces the construction cost by using the compartment of perforated caisson like using an air chamber.This innovation has both academic significance and important engineering value.For a new type of caisson,reliability analysis of the structure is necessary.Linear potential flow theory is applied to calculate the horizontal wave force acting on the caisson.The calculated results are compared with experimental data,showing the feasibility of the method.The Importance Sampling Procedure(ISP) is used to analyse the reliability of this caisson breakwater.展开更多
文摘This study examines the hydrodynamic performance of multiple-row vertical slotted breakwaters. We developed a mathematical model based on an eigenfunction expansion method and a least squares technique for Stokes second-order waves. The numerical results obtained for limiting cases of double-row and triple-row walls are in good agreement with results of previous studies and experimental results. Comparisons with experimental measurements of the reflection, transmission, and dissipation coefficients （CR, Cr, and CE） for double-row walls show that the proposed mathematical model adequately reproduces most of the important features. We found that for double-row walls, the CR increases with increasing wave number, kd, and with a decreasing permeable wall part, din. The Cr follows the opposite trend. The CE slowly increases with an increasing kd for lower kd values, reaches a maximum, and then decreases again. In addition, an increasing porosity of dm would significantly decrease the CR while increasing the Cr. At lower values of kd, a decreasing porosity increases the CE, but for high values of kd, a decreasing porosity reduces the Ce. The numerical results indicate that, for triple-row walls, the effect of the arrangement of the chamber widths on hydrodynamic characteristics is not significant, except when kd〈0.5 Double-row slotted breakwaters may exhibit a good wave-absorbing performance at kd〉0.5, where by the horizontal wave force may be smaller than that of a single wall. On the other hand, the difference between double-row and triple-row vertical slotted breakwaters is marginal.
基金supported by the National Natural Science Foundation of China (51279186,51479183)the 111 Project (B14028)The first author thanks the Chinese Scholarship Council for funding his research in University of Washington
文摘The reliability of a vertical breakwater is calculated using direct integration methods based on joint density functions.The horizontal and uplifting wave forces on the vertical breakwater can be well fitted by the lognormal and the Gumbel distributions,respectively.The joint distribution of the horizontal and uplifting wave forces is analyzed using different probabilistic distributions,including the bivariate logistic Gumbel distribution,the bivariate lognormal distribution,and three bivariate Archimedean copulas functions constructed with different marginal distributions simultaneously.We use the fully nested copulas to construct multivariate distributions taking into account related variables.Different goodness fitting tests are carried out to determine the best bivariate copula model for wave forces on a vertical breakwater.We show that a bivariate model constructed by Frank copula gives the best reliability analysis,using marginal distributions of Gumbel and lognormal to account for uplifting pressure and horizontal wave force on a vertical breakwater,respectively.The results show that failure probability of the vertical breakwater calculated by multivariate density function is comparable to those by the Joint Committee on Structural Safety methods.As copulas are suitable for constructing a bivariate or multivariate joint distribution,they have great potential in reliability analysis for other coastal structures.
基金supported by the National Natural Science Foundation of China (Grant No 4087-6047)
文摘The Oscillating Water Column(OWC) wave energy convertor with the advantage of its simple geometrical construction and excellent stability is widely employed.Recently,perforated breakwaters have been often used as they can effectively reduce the wave reflection from and wave forces acting on the structures.Considering the similarity between the compartment of perforated caisson and the air chamber of OWC wave energy convertor,a new perforated caisson of breakwater is designed in this paper.The ordinary caisson is modified by installing facilities similar to the air chamber of OWC converter,but here they are utilized to dissipate the wave energy inside the caisson.Such an arrangement improves the stability of the caisson and reduces the construction cost by using the compartment of perforated caisson like using an air chamber.This innovation has both academic significance and important engineering value.For a new type of caisson,reliability analysis of the structure is necessary.Linear potential flow theory is applied to calculate the horizontal wave force acting on the caisson.The calculated results are compared with experimental data,showing the feasibility of the method.The Importance Sampling Procedure(ISP) is used to analyse the reliability of this caisson breakwater.
