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.     

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.     

新型直立式透空堤消浪性能数值研究

为使防波堤同时具有良好的掩护效果和水体交换能力,提出了两种带有透浪通道的新型直立式防波堤。基于Fluent求解器建立了三维数值波浪水槽,通过与试验结果对比,验证了该数值水槽求解波浪与透空堤作用具有较高的精度。对两种防波堤在规则波作用下的透浪特性进行了研究,结果表明:透射系数K_t与透空率呈正线性相关,且可通过调整透浪通道间距,使相同透空率下K_t降低20%～30%。对同一结构,K_t随相对波长的增大而显著增大,但受相对波高的影响较小。在透空率大于0.16后,异型沉箱防波堤的消浪性能明显优于错位沉箱。基于数值计算结果,给出了以上两种透空堤波浪透射系数的经验公式。     

开孔双壁圆形钢吊箱围堰消波效果影响因素分析

跨海大桥桥墩基础施工若采用双壁钢围堰,则在其外壁进行开孔可有效减小波浪力,有利于降低钢围堰的制作造价和提高基础施工的安全性。以某跨海大桥基础施工采用的双壁圆形钢吊箱围堰为研究对象,引入波浪力折减系数K_d对消波效果进行评价,采用数值方法着重分析波浪参数和围堰自身结构设计参数对消波效果的影响规律。结果表明:K_d随波陡增大呈先快后缓的增大趋势,波陡超过0.032后,消波效果基本不再变化;随着相对水深的增大,K_d呈先减小后增大并趋缓的规律,在相对水深d/L约为0.455时取得最小值;K_d随开孔率的增大呈线性减小,开孔率越大,消波效果越好。随着双壁间距s的增大,K_d总体上呈减小趋势,且减小速率先快后慢;双壁间距较小时,开孔的消波作用较弱。开孔率和双壁间距两种因素间存在耦合作用,两者越大,其耦合作用也越强。围堰设计中可适当增大开孔率并选取合适的双壁间距以得到最佳消波效果。     

Wave interaction with twin plate wave barrier

The wave transmission and reflection characteristics and wave induced pressures on single surface plate and twin plate barriers were investigated experimentally for a wide range of wave heights and periods in regular and random waves. Seven different spacing between the plates were tested. It is found in general, hydrodynamically the twin plate is better than the single surface plate to reduce the wave transmission and increase the wave reflection. It is found that the transmission coefficient of twin plate reduced from 0.8 to 0.3 when the relative plate width is increased from 0.18 to 0.84. Transmission coefficient of twin plate barrier shows oscillating behavior, when relative plate width is increased due to blocking and pumping effect. The reflection coefficient increased from 0.25 to 0.65, when the relative width of the plate is increased from 0.18 to 0.84. The increase in spacing between the plates was also found to increase the reflection coefficient. The transmission coefficient, K_t for 98% probability of non-exceedence was found to be minimum and is about 0.60 when the relative spacing between the plate is about 0.12, compared to K_t=0.76 for single surface plate. The reflection coefficient for 98% probability of non-exceedence was found to exceed 0.66 for single surface plate, whereas it is 0.73 for twin plate with relative spacing of about 0.40. From the investigation with wide range of input parameters, it is found that the twin plate barrier needs to be designed for highest 98% pressure ratio of 2.0, which is equal to the static pressure induced by the design incident wave height.     

A model for wave growth in fetch-limited conditions

In this paper, it is held that the universal relationships of wave growth in fetch-limited conditions , i. e.,(f|~) p=A(x|~)-Band (m|~)0= C(x|~) Dshould satisfy the Toba 3/2 power law and the wave energy balance equation. In the ideal generation situation, theoretically it can be derived that the ideal fetch-limited wave growth relationship should have D=3B and D B =1, (i.e., B = 0.25, D = 0.75 ) and A3C=2. 1×l(T4C~(1/2)_d , where Cd is the drag coefficient. The 3/2 power law, the wave energy balance equation and the decrease of wave steepness with increasing fetch have became three requirements which should be satisfied by fetch-limited wave growth algorithms. A semi-empirical and semi-theoretical model for fetch-limited wave growth is presented. In the application to the slanting wind situation an un(?)ersal relationship of dimensionless wave energy vs dimensionless peak frequency is presented and the comparisons show that the model is in good agreement with observations.     

Wave interaction with T-type breakwaters

The wave transmission, reflection and energy dissipation characteristics of partially submerged ‘T'-type breakwaters (Fig. 1) were studied using physical models. Regular and random waves, with wide ranges of wave heights and periods and a constant water depth were used. Five different depths of immersions of the ‘T'-type breakwater were selected. The coefficient of transmission, K_t, coefficient reflection, K_r, were obtained from the measurements and the coefficient of energy loss, K_l is calculated using the law of conservation of energy. It is found that the coefficient of transmission generally reduces with increased wave steepness and increased relative water depth, d/L. This breakwater is found to be effective closer to deep-water conditions. K_t values less than 0.35 is obtained for both normal and high input wave energy levels, when the horizontal barrier of the T type breakwater is immersed to about 7% of the water depth. This breakwater is also found to be very efficient in dissipating the incident wave energy to an extent of about 65% (i.e. K_l>0.8), especially for high input wave energy levels. The wave climate in front of the breakwater is also measured and studied.

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Fig. 1. Schematic view of the T-type breakwater.     

Wave interaction with ‘’-type breakwaters

The wave transmission, reflection and energy dissipation characteristics of ‘’-type breakwaters were studied using physical models. Regular and random waves in a wide range of wave heights and periods and a constant water depth were used. Five different depths of immersion (two emerged, one surface flushing and two submerged conditions) of this breakwater were selected. The coefficient of transmission, K_t, and coefficient of reflection, K_r, were obtained from the measurements, and the coefficient of energy loss, K_l was calculated using the law of balance of energy. It was found that the wave transmission is significantly reduced with increased relative water depth, d/L, whether the vertical barrier of the breakwater is surface piercing or submerged, where ‘d’ is the water depth and ‘L’ is the wave length. The wave reflection decreases and energy loss increases with increased wave steepness, especially when the top tip of the vertical barrier of this breakwater is kept at still water level (SWL). For any incident wave climate (moderate or storm waves), the wave transmission consistently decreases and the reflection increases with increased relative depth of immersion, Δ/d from −0.142 to 0.142. K_t values less than 0.3 can be easily obtained for the case of Δ/d=+0.071 and 0.142, where Δ is the height of exposure (+ve) or depth of immersion (−ve) of the top tip of the vertical barrier. This breakwater is capable of dissipating wave energy to an extent of 50–80%. The overall performance of this breakwater was found to be better in the random wave fields than in the regular waves. A comparison of the hydrodynamic performance of ‘’-type and ‘T’-type shows that ‘T’-type breakwater is better than ‘’-type by about 20–30% under identical conditions.     

双消浪室局部开孔沉箱防波堤反射特性的理论与试验研究

双消浪室局部开孔沉箱防波堤具有低反射、结构受力小、适宜较大水深和工程造价低等优点。为明确双消浪室局部开孔沉箱水动力特性的主要影响因素,采用理论分析和物理模型试验相结合的方法,对规则波和不规则波作用下双消浪室局部开孔沉箱防波堤的反射特性进行研究。基于势流理论,建立规则波和不规则波对局部开孔沉箱防波堤作用的三维解析解,采用二次压力损失边界条件考虑沉箱开孔墙对波浪运动的影响,利用周期性边界条件考虑防波堤结构沿长度方向的周期性变化。开展相应规则波和不规则波物理模型试验,验证理论模型的合理性。通过算例分析,研究不同波浪要素和结构参数对防波堤反射特性的影响。研究表明:双消浪室局部开孔沉箱相对消浪室宽度取值为0.08~0.20,沉箱前墙开孔率大于后墙开孔率时,防波堤在较大波浪频率范围内消波效果显著;当前后墙的开孔率相等时,防波堤反射系数的最小值随着开孔率增大而减小。     

Experimental study on the performance of twin plate breakwater

The wave transmission characteristics and wave induced pressures on twin plate breakwater are investigated experimentally in regular and random waves.A total of twenty pressure transducers are fixed on four surfaces of twin plate to measure the wave induced dynamic pressures.The spatial distribution of dynamic wave pressure is given along the surface of the twin plate.The uplift wave force obtained by integrating the hydrodynamic pressure along the structure is presented.Discussed are the influence of different incident wave parameters including the relative plate width B /L,relative wave height /i H a and relative submergence depth s /a on the non-dimensional dynamic wave pressures and total wave forces.From the investigation,it is found that the optimum transmission coefficient,t K occurs around B /L 0.41 ~ 0.43,and the twin plate breakwater is more effective in different water depths.The maximum of pressure ratio decreases from 1.8 to 1.1 when the relative submergence depth of top plate is increased from 0.8to +0.8.     

Dependence of sea surface drag coefficient on wind-wave parameters

The relationships between sea surface roughness z 0 and wind-wave parameters are analyzed,and spurious self-correlations are found in all of the parameterization schemes.Sea surface drag coefficient C D is fitted by four wind-wave parameters that are wave age,wave steepness,windsea Reynolds number R B and R H ,and the analyzed data are divided into laboratory,field and combined data sets respectively.Comparison and analysis of dependence of C D on wind-wave parameters show that R B can fit the C D most appropriately.Wave age and wave steepness are not suitable to fit C D with a narrow range data set.When the value of wave age has a board range,R H is not suitable to fit C D either.Three relationships between C D and R B are integrated into the bulk algorithm COARE to calculate the observational friction velocity,and the results show that the relationship between C D and R B which is fitted with field data set can describe the momentum transfer in the open ocean,under low-moderate wind speed condition,most appropriately.     

Hydrodynamic Coefficients for Grouping Piles Under the Action of Irregular Waves

-The hydrodynamic coefficients for each of two piles and three piles in both side-by-side arrangement and tandem arrangement under the action of irregular waves are experimentally investigated. These coefficients vary with the KC number, the relative pile spacing, the number of piles and the pile location, and their relationships are presented in this paper. They can be used in Morison Equation and other equations to calculate directly the in-line wave forces and the transverse forces on each pile in array.     

Geometrical properties of perfect breaking waves on composite breakwaters

The experimental results have so far shown that when a wave breaks on a vertical wall with an almost vertical front face at the instant of impact that is called perfect breaking or perfect impact, the greatest impact forces are produced on the wall. Therefore, the configuration of breaking waves is important in the design considerations of coastal structures. The present study is concerned with determining the geometrical properties of oscillatory waves that break perfectly on the vertical wall of composite-type breakwaters. The laboratory tests for perfect breaking waves on composite breakwaters are conducted with base slopes of 1/2, 1/4 and 1/6, and with berm widths of 0.00, 0.10, 0.20, 0.30 and 0.40 m. The shape and the dimensions of waves at the instant of perfect breaking on the wall are determined using a video camera. The experimental results for the geometrical properties of the breakers are presented non-dimensionally. Within the range of present experimental conditions, it is found that the dimensionless breaker crest height, h_b/d_w, and dimensionless breaker height, H_b/d_w, decrease; and, dimensionless breaker depth, d_w/H₀, increases with increasing relative berm width, B/D. The breaker height index, H_b/H₀, is almost unaffected by B/D. The deep-water wave steepness and the base slope of the breakwater do not seem to influence the geometrical properties of the breakers at wall systematically.     

Performance of solid and perforated U-type breakwaters under regular and irregular waves

An experimental investigation of U-type breakwaters was carried out in a laboratory channel. Both regular and irregular waves were used during testing. Two types of breakwaters such as solid and perforated were studied to analyse the porosity effect of structures. In order to investigate performance of these breakwaters for different immersion depths, four depths of immersions of the solid and perforated breakwaters were selected. Different wave groups were generated over these breakwaters, and the transmission, reflection and energy dissipation characteristics of each breakwater were determined. Three coefficients such as transmission, reflection and energy dissipation coefficients, which were named as C_t, C_r, and C_l, respectively, were used during the evaluation of the test results. The most important parameters governing performance of these breakwaters were determined by using earlier investigations and experimental results. These parameters were expressed as a dimensionless group by using π theory. Based on the test results, empirical expressions were formulated to describe the C_t, C_r, and C_l for different immersion depths of solid and perforated breakwaters under regular and irregular waves.     

Reinforcement and Arching Effect of Geogrid-Reinforced and Pile-Supported Embankment on Marine Soft Ground

The effectiveness of constructing a geogrid-reinforced and pile supported embankment on soft ground to reduce differential settlement has been studied by pilot scale field tests and numerical analysis. Three-by-three pile groups with varying pile spacing were driven into a layer of soft ground, and a layer of geogrid was used as reinforcement over each pile group. Further, a 2-D numerical analysis has been conducted using the computer program FLAC 2D. The mechanisms of load transfer can be considered as a combination of embankment soil arching, geogrid tension, and stress transfer due to the difference in stiffness between pile and soft ground. Based on the pilot scale field tests and results of numerical analysis, we find that the geosynthetic reinforcement slightly interferes with soil arching, and helps reduce differential settlement of the soft ground. Also, the most effective load transfer and vertical stress reduction at the midspan between piles occurs when the pile cap spacing index D/b (D: pile cap spacing, b: diameter of pile) is 3.0.     

Wave reflection and transmission by curtainwall–pile breakwaters using circular piles

This paper presents a mathematical model which computes the hydrodynamic characteristics of a curtainwall–pile breakwater (CPB) using circular piles, by modifying the model developed for rectangular piles by Suh et al. [2006. Hydrodynamic characteristics of pile-supported vertical wall breakwaters. Journal of Waterway, Port, Coastal and Ocean Engineering 132(2), 83–96]. To examine the validity of the model, laboratory experiments have been conducted for CPB with various values of draft of curtain wall, spacing between piles, and wave height and period. Comparisons between measurement and prediction show that the mathematical model adequately reproduces most of the important features of the experimental results. The mathematical model based on linear wave theory tends to over-predict the reflection coefficient as the wave height increases. As the draft of the curtain wall increases and the porosity between piles decreases, the reflection and transmission coefficient increases and decreases, respectively, as expected. As the relative water depth increases, however, the effect of porosity disappears because the wave motion is minimal in the lower part of a water column for short waves.     

Hydrodynamic performance of double rows of piles suspending horizontal c shaped bars

The wave transmission, reflection, and energy dissipation of the double rows of vertical piles suspending horizontal steel C shaped bars are experimentally and theoretically studied under normal regular waves. Different wave and structural parameters are investigated e.g. the wave length, the C shaped bars draft and spacing, the supporting piles diameter and spacing, and the space between the double rows. Also, the theoretical model based on an eigenfunction expansion method is developed to study the hydrodynamic breakwater performance. In order to examine the validity of the theoretical model, the theoretical results are compared with the experimental and theoretical results obtained by different authors. Comparison between experiments and predictions showed that theoretical model provides a good estimate to the different hydrodynamic coefficients when the friction factors of the upper and the lower parts are f_U = 1.5 and f_L = 0.75. The present breakwater physical model gives efficiency near other similar systems of different shapes.     

Effect of under connected plates on the hydrodynamic efficiency of the floating breakwater

In this paper, the hydrodynamic efficiency of a floating breakwater system is experimentally studied by use of physical models. Regular waves with wide ranges of wave heights and periods are tested. The efficiency of the breakwater is presented as a function of the wave transmission, reflection, and energy dissipation coefficients. Different parameters affecting the breakwater efficiency are investigated, e.g. the number of the under connected vertical plates, the length of the mooring wire, and the wave length. It is found that, the transmission coefficient kt decreases with the increase of the relative breakwater width B/L, the number of plates n and the relative wire length l/h, while the reflection coefficient kr takes the opposite trend. Therefore, it is possible to achieve kt values smaller than 0.25 and kr values larger than 0.80 when B/L is larger than 0.25 for the case of l/h-1.5 and n=4. In addition, empirical equations used for estimating the transmission and reflection coefficients are developed by using the dimensionless analysis, regression analysis and measured data and verified by different theoretical and experimental results.     

Modified McCormicks model for equilibrium shorelines behind a detached breakwater

Experimental data of equilibrium shorelines behind a detached breakwater obtained by previous investigators were collected and re-reviewed to investigate the major parameters affecting the shoreline shapes. The result shows that the equilibrium shorelines depend not only on the breakwater length B and the distance of the breakwater from the initial shoreline S, but also on the incident wave steepness H₀/L₀, beach slope S_b and the sand size D₅₀. Most of equilibrium shorelines behind a detached breakwater could be approximately described by a couple of elliptic curves as proposed by McCormick (Ports, Coastal & Ocean Engineering ASCE 119, 1993, p. 657). However, after re-examination, this paper shows that the dimensionless semiminor axis b/S and the dimensionless distance G/b in the McCormick’s elliptic-curve model should be modified, as compared with the available experimental data. The modified expressions of b/S and G/b were proposed, and the performances of the modified expressions were also detaily examined in this paper.     

Mooring forces in horizontal interlaced moored floating pipe breakwater with three layers

The paper presents the results from model scale experiments on the study of forces in the moorings of horizontally interlaced, multi-layered, moored floating pipe breakwaters. The studies are conducted with breakwater models having three layers subjected to waves of steepness H_i/L (H_i is the incident wave height and L the wavelength) varying from 0.0066 to 0.0464, relative width W/L (W is the width of breakwater) varying from 0.4 to 2.65, and relative spacing S/D (S is the spacing of pipes and D the diameter of pipe) of 2 and 4. The variation of measured normalized mooring forces on the seaward side and leeward side are analyzed by plotting non-dimensional graphs depicting f/γW² (f is the force in the mooring per unit length of the breakwater, γ the weight density of sea water) as a function W/L for various values of H_i/d (d is the depth of water). It is found that the force in the seaward side mooring increases with an increase in H_i/L for d/W values ranging between 0.081 and 0.276. The experimental results also reveal that the forces in the seaward side mooring decrease as W/L increases, up to a value of W/L=1.3, and then increases with an increase in W/L. It is also observed that the wave attenuation characteristics of breakwater model with relative spacing of 4 is better than that of the model with relative spacing of 2. The maximum force in the seaward side mooring for model with S/D=4 is lower compared to that for the breakwater model with S/D=2. A multivariate non-linear regression analysis has been carried out for the data on mooring forces for the seaside and leeside.