Derivation of unified wave overtopping formulas for seawalls with smooth,impermeable surfaces based on selected CLASH datasets

A set of unified formulas for prediction of the mean rate of wave overtopping at coastal structures with smooth, impermeable surfaces have been derived through the analysis of the selected CLASH datasets. The mean wave overtopping rate is expressed as the function of the significant wave height at the structural toe and the relative freeboard. The formulas are applicable for both vertical walls and inclined seawalls with smooth transition between them. The formulas are simple but cover the full range of water depth from the shoreline to deep water. The effects of the toe depth and the seabed slope on wave overtopping rate are duly incorporated in the formulas. Prediction performance of the new formulas is better than the EurOtop formulas for both vertical walls and inclined seawalls.     

An investigation of breaking wave pressures on inclined walls

Shoreline structures are subjected to breaking wave loads which may reach 690 KN/m². One possibility to reduce these loadings is to slope the exposed surface backwards. The possible amount of reduction in breaking wave loads is, however, unclear, and recent model tests indicated that sloped walls might be exposed to higher loads than are vertical walls. Within the Wave Energy Group at Queen's University Belfast, tests on a 1/36 model of a shoreline wave power station were conducted in order to assess the influence of front wall inclination on the magnitude of breaking wave pressures. It was found that breaking wave pressures decrease from 100% for the vertical wall to 44% for a 32.7° backwards inclined wall and to 64% for a 32.7° forward inclined wall. From the results it was concluded that a maximum pressure of 105% can be expected for a 10° forward inclined wall. Design recommendations were found to be conservative.     

Wave reflection characteristics of plane, dentated and serrated seawalls

The hydrodynamic performance of vertical and sloped plane, dentated and serrated seawalls were investigated using physical model studies. Regular and random waves of wide range of heights and periods were used. Tests were carried out for different inclinations of the seawall (i.e. θ=30, 40, 50, 60 and 90°) and for a constant water depth of 0.7 m. The wave reflection was measured to assess the dissipation character of the seawalls. It was observed that the serrated seawall was superior to the plane and dentated seawall in reducing the wave reflection. Even for the vertical case, the coefficient of reflection due to regular waves for dentated seawall ranged from 0.6–0.99 and for the vertical serrated seawall it was 0.45–0.98, whereas for the vertical plane wall, it was almost 1.0. It was found that the characteristic dimension of the seawall (i.e. L/W) and the relative water depth (i.e. d/L) were better influencing parameters compared to the conventionally used surf similarity parameter ‘ξ’ (ξ=tan θ/(H_i/L)^0.5) in predicting the reflection from the dentated and serrated seawall, where L is the local wave length, W the width of the dent along the length of the seawall slope, d the water depth at the toe and H_i is the incident wave height. A similar trend was observed for the random waves too. The reduction in the wave reflection due to random waves for the dentated seawall as compared to the plane seawall was about 18% and for the serrated seawall, it was 20%. It was observed that the reflection due to random waves was lesser for all the three different walls than the regular waves, due to the mutual interaction of random waves. Multiple regression analysis on the measured data points was carried out and predictive equations for the reflection coefficient were obtained for both regular and random waves. This study will be useful in the design of energy dissipating type vertical quay walls in ports and harbours, sloped seawalls for shore protection from erosion and sloped caisson as breakwaters. Comparison of predictive formulae with the experimental results revealed that the prediction methods were good enough for practical purposes.     

Experimental investigating on the reflected waves from the caisson-type vertical porous seawalls

The hydrodynamic efficiencies of caisson-type vertical porous seawalls used for protecting coastal areas were calculated in this study. Physical models were developed to compare the wave reflection from vertical plane, semi-porous, and porous seawalls caused by both regular and random waves. Tests were carried out for a wide range of wave heights, wave periods, and different water depths (d=0.165, 0.270 and 0.375 m). The performance regarding the reflected waves from porous and semi-porous seawalls showed improvement when compared with those from the plane seawall. The reflection coefficients of the porous and semi-porous seawalls were calculated as 0.6 and 0.75, respectively, while the coefficient for the fully reflecting plane vertical wall was significantly higher (0.9). It was also observed that the reflection coefficient decreases with increase in wave steepness and relative water depth. In addition, the reduction in the reflection coefficient of porous and semi-porous seawalls, as compared to that of a plane seawall, was observed for both regular and random waves. New equations were also proposed to calculate the reflection coefficient of different types of seawalls with the aid of laboratory experiments. By verifying the developed equations using some other experimental data, it was validated that the equations could be used for practical situations. The results of the present study can be applied to optimize the design of vertical seawalls and for coastal protecting schemes.     

Evaluation of wave impact loads on caisson breakwaters based on joint probability of impact maxima and rise times

When waves break against seawalls, vertical breakwaters, piers or jetties, they abruptly transfer their momentum into the structure. This energy transfer is always spectacular and perpetually unrepeatable but can also be very violent and affect the stability and the integrity of coastal structures. Over the last 15 years, increasing awareness of wave-impact induced structural failures of maritime structures has emphasised the need for a more complete approach to dynamic responses, including effects of impulsive loads. At the same time, movement of design standards toward probabilistic approaches requires new statistical tools able to account for uncertainties in the variability of wave loading processes. This paper presents a new approach to the definition of loads for use in performance design of vertical coastal structures subject to breaking wave impacts.     

Extreme wave run-up and pressure on a vertical seawall

The performance of coastal vertical seawalls in extreme weather events is studied numerically, aiming to provide guidance in designing and reassessing coastal structures with vertical wall. The extreme wave run-up and the pressure on the vertical seawall are investigated extensively. A time-domain higher-order boundary element method (HOBEM) is coupled with a mixed Eulerian-Lagrangian technique as a time marching technique. Focused wave groups are generated by a piston wave-maker in the numerical wave tank using a wave focusing technique for accurately reproducing extreme sea states. An acceleration-potential scheme is used to calculate the transient wave loads. Comparisons with experimental data show that the extended numerical model is able to accurately predict extreme wave run-ups and pressures on a vertical seawall. The effects of the wave spectrum bandwidth, the wall position and the wave nonlinearity on the wave run-up and the maximum wave load on the vertical seawall are investigated by doing parametric studies.     

Analysis Procedure of the Cyclic Bearing Capacity for Suction Anchors in Soft Clays

This article presents a procedure to calculate the bearing capacity of suction anchors subjected to inclined average and cyclic loads at the optimal load attachment point using the undrained cyclic shear strength of soft clays based on the failure model of anchors proposed by Andersen et al. The constant average shear stress of each failure zone around an anchor is assumed and determined based on the static equilibrium condition for the procedure. The cyclic shear strength of each failure zone is determined based on the average shear stress. The cyclic bearing capacity is finally determined by limiting equilibrium analyses. Thirty-six model tests of suction anchors subjected to inclined average and cyclic loads were conducted, which include vertical and lateral failure modes. Model test results were predicted using the procedure to verify its feasibility. The average relative error between predicted and test results is 1.7%, which shows that the procedure can be used to calculate the cyclic bearing capacity of anchors with optimal loading. Test results also showed that the anchor was still in vertical failure mode under combined average and cyclic loads if an anchor was in vertical failure mode under static loads. The anchor failure would depend on the vertical resistance degradation under cyclic loads if an anchor was in lateral failure mode under static loads. Cyclic bearing capacities associated with the number of load cycles to failure of 1000 were about 75% and 80% of the static bearing capacity for vertical failure anchors and lateral failure anchors, respectively.     

Assessment of boundary-element method for modelling a free-floating sloped wave energy device. Part 1: Numerical modelling

The boundary-element method has been widely used as a design tool in the offshore and ship building industry for more than 30 years. Its application to wave energy conversion is, however, more recent. This paper deals with the numerical modelling of a free-floating sloped wave energy device. The power take-off mechanism of the device consists of an immersed tube with a piston sliding inside. The modelling is done using the boundary-element method package WAMIT. The model is first worked out for the case where the axis of the tube is vertical. It is then derived for the tube inclined and successfully verified against numerical benchmark data. A companion paper presents results of a detailed comparison with a physical model study.     

Experimental Study on Stability of Breakwaters with Penetrating Box Foundations

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Seismic Stability of Gravity Retaining Structures by Pseudo-Dynamic Method

An analytical expression of a gravity retaining wall's seismic stability against sliding and overturning is proposed in this article. The derivation, aiming at the cohesionless soil with inclined backfill surface and nonvertical wall back, is based on limit equilibrium analysis and the pseudo-dynamic method. The variations of the sliding and overturning stability safe factors with the horizontal seismic acceleration are investigated for different seismic amplification factors, soil friction angles, wall friction angles, vertical seismic acceleration coefficients, wall back inclination angles, and backfill surface inclination angles. The results indicate that the soil friction and horizontal seismic action significantly impact the seismic stability. The increase of vertical earthquake action changes the curvature of stability factor curves. The wall friction and back inclination strengthen the gravity retaining wall's resistance to sliding and overturning failure while the backfill surface inclination plays a negative role in the seismic stability. We also found that the seismic stability safe factors calculated by the proposed method are larger but more reasonable than those by the Mononobe-Okabe method.     

组合桶形基础水平循环承载力模型试验

在一个大型土池中进行了软土中组合四桶基础在竖向静荷载与水平循环荷载共同作用下的承载力模型试验,研究了竖向静荷载与水平循环荷载对组合桶形基础破坏形式与承载力的影响。试验结果表明,组合四桶基础的变形主要包括水平循环变形与竖向循环累积沉降。基础的破坏形式取决于水平循环荷载与竖向静荷载。若竖向静荷载较小,过大的水平循环位移将导致基础破坏;随竖向静荷载增加,竖向循环累积沉降将变为导致基础破坏的主要原因。试验结果还表明,在不同竖向静荷载与水平循环荷载共同作用下,基础的水平循环承载力大约为水平静承载力的70%左右。     

斜坡堤典型胸墙波浪力的影响因素

为探求斜坡堤典型胸墙迎浪面所受波浪力大小的影响因素,设计前仰式、深弧式、后仰式和直立式4种结构型式胸墙进行相关的物理模型试验。通过在典型胸墙迎浪面间隔布置压力测点,获取所受波浪压力,并将其进行积分求和,得到胸墙所受波浪力,进而讨论相对波高、相对波长、斜坡坡度和胸墙结构型式对波浪力的影响。结果表明,相对波高与相对波长对胸墙所受波浪力影响显著;波浪力随着相对波高的增大而增大,随着相对波长的增大呈现先增大、后减小、再增大的变化趋势;波浪力随着斜坡坡度的增大而减小。斜坡堤弧形胸墙所受波浪力明显大于直立式胸墙所受波浪力;在斜坡堤弧形胸墙中,前仰式胸墙受力较其余两种型式胸墙受力小。研究结果将加深波浪对斜坡堤胸墙作用力的理解,为后续工程设计提供理论指导。     

Bed changes at toe of inclined seawalls

This study was carried out to investigate the scour phenomenon at the toe of seawalls and the different parameters that affected it. Experiments were achieved using different wave steepnesses, bed material grain sizes, wall positions and inclinations. Based on experimental results, the parametric plots of toe scour for smooth impermeable inclined seawalls were prepared. Also, this paper presents the bed changes prediction at seawalls toe using artificial neural networks on the basis of experimental data to widen the range of application. Suitability of using a neural network model was developed, and a model was validated. It is proposed that this model can be used in coastal engineering applications.     

Prediction of wave pressures on smooth impermeable seawalls

Simple prediction methods are proposed to estimate the wave induced pressures on smooth impermeable seawalls. Based on the physics of the wave structure interaction, the sloped seawall is divided into a total of five zones (zones 1, 2 and 3 during run-up (corresponding pressures are called as positive pressures) and zones 4 and 5 during run-down (corresponding pressures are called negative pressures)) (Fig. 1). Zone 1 (0<z<d−H_i/2), where the wave pressure is governed by the partial reflection and phase shift; Zone 2 (d−H_i/2<z<d), where the effect of wave breaking and turbulence is significant; Zone 3 (d<z<Run-up height), where the pressure is induced by the run-up water; Zone 4 (Run-down<z<d), where the wave pressure is caused by the run-down effect and Zone 5 (0<z<d-Run down), where the negative wave pressures are due to partial reflection and phase shift effects. Here d is the water depth at the toe of the seawall, H_i is the incident wave height and z is the vertical elevation with toe of the seawall as origin and z is positive upward. For wave pressure prediction in zones 1 and 5, the empirical formula proposed by Ahrens et al. (1993) to estimate the wave reflection and Sutherland and Donoghue's recommendations (1998) for the estimation of phase shift of the waves caused by the sloped structures are used. Multiple regression analysis is carried out on the measured pressure data and empirical formulas are proposed for zones 2, 3 and 4. The recommendations of Van der Meer and Breteler (1990) and Schüttrumpf et al. (1994) for the prediction of wave run-down are used for pressure prediction at zone 4. Comparison of the proposed prediction formulas with the experimental results reveal that the prediction methods are good enough for practical purposes. The present study also shows a strong relation between wave reflection, wave run-up, wave run-down and phase shift of waves on wave pressures on the seawalls.     

斜坡堤典型胸墙波浪力影响因素的试验与分析

为探求斜坡堤典型胸墙迎浪面所受波浪力大小的影响因素,设计前仰式、深弧式、后仰式和直立式四种结构型式胸墙进行相关的物理模型试验。通过在典型胸墙迎浪面间隔布置压力测点获取所受波浪压力,并将其进行积分求和得到胸墙所受波浪力,进而讨论相对波高(H/d)、相对波长(L/d)、斜坡坡度和胸墙结构型式对波浪力的影响。试验结果表明：相对波高与相对波长对胸墙所受波浪力影响显著。波浪力随着相对波高的增大而增大,随着相对波长的增大呈现先增大—后减小—再增大的变化趋势。波浪力随着斜坡坡度的增大而减小。斜坡堤弧形胸墙所受波浪力明显大于直立式胸墙所受波浪力;在斜坡堤弧形胸墙中,前仰式胸墙受力较其余两种型式胸墙受力小。研究结果将加深波浪对斜坡堤胸墙作用力的理解,为后续工程设计提供理论指导。     

Centrifuge modelling of caisson breakwater subject to wave-breaking impacts

Model tests were conducted to investigate the behaviour of caisson breakwater resting on sand beds subject to impacts due to wave breaking. The centrifuge modelling technique was employed to simulate the prototype stress levels in the foundation soil as the behaviour of sand is highly stress dependent. A wave actuator was developed to simulate the wave-breaking impact loads on the caisson during centrifuge flight. The test results reveal that the vertical and horizontal movements and tilt of the caisson breakwater increase progressively with the number of breaking-wave impacts. The excess pore pressures developed in the foundation sand under non-reversal loading are generally small and appear insignificant. The results of the parametric studies conducted to examine the effects of impact-load pattern, caisson width, rock berm beneath caisson, wave slamming on top slab of caisson and cyclic preloading on the performance of caisson breakwater are also presented. The practical implications of the experimental findings in the present study are also highlighted in this paper.     

软土地基沉箱防波堤失稳模式及稳定性分析方法

针对现阶段深水软黏土地基防波堤建设的设计理论和稳定性分析方法尚不成熟,结合实际工程,采用三维弹塑性有限元数值分析方法,研究在水平或竖直单一方向荷载以及复合加载条件下软黏土地基上沉箱防波堤的失稳模式,提出破坏包络线的稳定性判别方法。在波浪水平荷载作用下,深水软基上沉箱防波堤发生倾覆失稳破坏,失稳转动点为沉箱底面以下中轴线偏右的某点,不同于规范中规定的岩石或砂质地基沉箱倾覆转动点为其后踵点;在重力等竖向荷载作用下,沉箱的失稳模式为结构整体下陷,抛石基床及地基形成连贯的塑性区域,呈现较明显地冲剪破坏形式;在水平、竖向复合荷载作用下,软基上沉箱防波堤的破坏包络线由结构倾覆破坏线和地基承载力破坏线组成,包络线将荷载组合区分成稳定区、仅发生水平承载力不足倾覆破坏区、仅发生地基竖向承载力不足破坏区、同时发生水平承载力和地基竖向承载力不足破坏区4个区域。研究成果为深水软基沉箱防波堤建设提供参考和借鉴。     

Experimental evaluation of early patterns of colonisation of space on rocky shores and seawalls

The introduction of artificial structures in coastal areas can cause fragmentation and loss of natural habitats. Previous studies found that variation in colonisation of space at mid-shore levels could account for differences in mature assemblages between seawalls and vertical surfaces on adjacent rocky shores in Sydney Harbour (Australia). This study tests the model that the nature of the substratum is responsible for different patterns of early colonisation between vertical ledges of rocky shores and seawalls. According to this model, patterns in early colonisation would differ between cleared areas created on vertical surfaces on rocky shores and seawalls, but not between standard surfaces (panels) installed on each structure. Early colonisation of space differed between seawalls and rocky shores, regardless of the type of substratum (clearings versus panels). Differences in relative abundances between structures were evident on both types of substrata for some taxa, while they varied between substrata for others. No taxa, however, showed consistent differences between structures in only the clearings. In addition, the abundance of some taxa differed between panels on the different structures, suggesting that the effects of the substratum were modulated by factors operating differentially between rocky shores and seawalls.     

Wave loads on rubble mound breakwater crown walls in deep and shallow water wave conditions

The semi-empirical formulae by Pedersen (1996) for wave loads on vertical front faces of stiff crown walls are based on model tests with deep and intermediate water wave conditions. A new series of model tests performed at the same test facility as used by Pedersen has revealed that the formulae by Pedersen overpredict the loads in shallow water wave conditions. This paper presents a modification/expansion of the formulae to cover loads in both deep and shallow water wave conditions. The modification is based on a series of 162 physical model tests on typical rubble mound breakwaters with crown wall superstructures. The implementation of shallow water wave conditions in the formulae is done by modifying the term for wave run-up to be dependent on the incident wave height distribution. Moreover, the adjusted formulae provide more accurate estimates of the wave loads on free walls without front armour protection. Pressure transducers with very high eigen-frequencies were used in the present model tests as opposed to the transducers applied by Pedersen which in some cases seem to have been affected by dynamic amplifications.     

Reliability-based assessment and design of stone-filled crib seawalls for shoreline protection

In this study, an efficient reliability-based design tool for stone-filled crib seawalls is developed. The first-order reliability method is integrated into spreadsheet to facilitate the reliability analysis for practical application. Using this spreadsheet tool, the effects of several major uncertain factors on the seawall design, including design water level, material property, and wave forces, are explicitly explored. In addition, the impact of progressive scour on the seawall stability is demonstrated through a time-dependent reliability analysis. This developed reliability-based design tool for seawalls is validated through comparing with the Monte Carlo simulation. This seawall design tool is easy to use and can be readily adapted in various aspects in the seawall design for shoreline protection.