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In this paper, the occurrence rate of caisson sliding of a vertical breakwater during a storm and the probabilistic distribution of the individual sliding distances are derived as functions of such important design variables as water depth, significant wave height, and caisson width. The expressions for various representative sliding distances such as the significant sliding distance are also derived. The derived statistical characteristics of individual sliding distances are then used for calculating the first passage probability of an allowable individual sliding distance during a storm. A method is also proposed to calculate the time-dependent first passage probability for the case where wave climate and mean water depth change with time. Finally, tentative design criteria for the allowable individual sliding distance are proposed. The proposed method is applied to fictitious breakwaters in different water depths near the Port of Hitachinaka in Japan. The time-dependent first passage probability is calculated for the next 50 years in which the wave height may increase due to climate change. The first passage probability increases as time elapses, as the water depth increases, and as the allowable individual sliding distance decreases. Comparison with a previous study that uses a performance-based design method shows that the allowable first passage probability should be in the range between 0.05 and 0.09. For the proposed method to be used in a practical design, however, more detailed study should be made to determine the allowable values of individual sliding distance, first passage probability, and representative sliding distance, by comparing with current design methods. [ABSTRACT FROM AUTHOR]

Abstract: The effects of long-term sea-level rise and offshore wave-height increase due to climate change on the stability of caisson breakwaters constructed in different water depths are analyzed by using a time-dependent performance-based design method. An artificial neural network is combined with the wave transformation model to reduce the computation time in the Monte Carlo simulation. The breakwater is designed by the conventional safety-factor method, while its performance is evaluated by the expected sliding distance. In general, the stability of the breakwater is reduced if the climate change effects are included, but it shows different trends depending on water depth. Outside the surf zone, the effect of sea-level rise decreases with increasing water depth, whereas that of wave-height increase increases with water depth. Inside the surf zone, however, both effects decrease with decreasing water depth, with greater effect of wave-height increase than sea-level rise. In the design of a caisson breakwater of ordinary importance, it is not necessary to take into account the effect of sea-level rise, whereas the effect of wave-height increase should be taken into account if the breakwater is constructed far outside the surf zone. However, it should be noted that different results should be obtained if the breakwater were designed based on the expected sliding distance. [Copyright &y& Elsevier]

In the probabilistic design of a breakwater armor layer, it is often necessary to calculate the damage accumulated over the breakwater's life cycle. In this paper, a comparison is made between existing methods to calculate the cumulative damage to the breakwater armor layer. In the current study, hydraulic experiments are conducted to gauge the damage progression of Tetrapod armor units. When severe damage occurs at the beginning of the breakwater's life cycle, the two methods do not differ significantly, but, in general, the latter predicts a larger cumulative damage than the former. For a Tetrapod armor layer, it is recommended that the average of the two methods be used. [ABSTRACT FROM AUTHOR]

Abstract: During the last decade, partial safety factor systems have been adopted in the design standards of coastal structures, which are based on probabilistic theories but have a format similar to the traditional safety factor system. Tetrapod is one of the widely used breakwater armor units in the world. The previous partial safety factor system was developed based on limited wave and structure data in several locations. In this paper, a partial safety factor system for Tetrapod armor units is developed by performing reliability analysis and optimal code calibration for 116 breakwater cross-sections and wave conditions in 31 harbors in Korea. The partial safety factors associated with different ranges of the shape parameter of the Weibull extreme wave height distribution for different target probabilities of failure are proposed. For other types of extreme distributions, the skewness of the distribution should be calculated and the partial safety factors of the Weibull distribution of the same skewness could be used (the skewness of the Weibull distribution changes with the shape parameter). The developed system is applied to existing breakwaters to examine its applicability. [Copyright &y& Elsevier]

This paper presents a method to incorporate the effect of climate change on the performance-based design of a caisson breakwater and its application to the East Breakwater of the Port of Hitachinaka in Honshu, Japan. The up-to-date projection estimated a future sea-level rise of 0.25-0.6 m and a wave-height increase of 1.7 m (from 8.3 to 10 m) during the 21st century in this area. The influence of a sea-level rise on caisson sliding was minimal; the sea-level rise was much smaller than the water depth at the breakwater site. When the effects of climate change were not included, the performance-based design method calculated the same caisson width as that of the constructed breakwater, partly validating the consistency between conventional deterministic methods and performance-based design methods. The effects of climate change dictate an increase in caisson width of approximately 1.5 and 0.5 m for linear and parabolic increases of wave height, respectively, which are approximately 6.8 and 2.3% of the present caisson width of 22 m. Finally, it is recommended that the caisson breakwater be designed using the projected wave height and water level in 30 years from construction, if the deterministic design method is used and the effects of climate change are to be taken into account. [ABSTRACT FROM AUTHOR]

Abstract: This paper presents two methods that evaluate the target reliability of caisson sliding of a vertical breakwater. First, the statistical characteristics and probability density function are obtained for the safety factors of the breakwaters designed by deterministic methods in the past. The first method calculates the probability density of reliability index by applying the Monte Carlo simulation to the safety factor for various combinations of uncertainties of load and resistance. The significant target reliability index is then calculated by averaging the highest one third of the reliability index. The second method uses the Chebyshev inequality which describes the lower limit of reliability index. Again the Monte Carlo simulation is used to calculate the probability density of the lower limit of reliability index. The maximum of the possible lower limits is then taken as the target reliability index. The application of the methods has given the target reliability indices close to one another and also close to the value used in a recently published design standard. [Copyright &y& Elsevier]

In Korea, Tetrapods have been widely used to protect rubble mound breakwaters against erosion due to wave action. The deterministic design method has been used based on Hudson or van der Meer formula. In this study, we have performed reliability analyses for thus designed Tetrapod armors of 12 trade harbors and 8 coastal harbors in Korea. It is found that there is a linear relationship between the safety factor and the probability of failure; the larger the safety factor, the smaller the probability of failure. It is also found that the probability of failure during 50-year service lifetime is about 60% for the Tetrapod armors designed by the deterministic design method with the safety factor of 1.0. This finding seems to be natural since the encounter probability that a breakwater will experience storm waves greater than the design wave during its lifetime is 63% if the lifetime is set equal to the design return period. The results of this study could provide a guideline for determining the target probability of failure of Tetrapod armors in the future. A similar approach could be used for armor units other than Tetrapods. [ABSTRACT FROM AUTHOR]

In calculating the partial safety factors of breakwater armor stones, it has been assumed that all the design variables are independent of one another. However, some of them are not independent but are correlated to each other. In the present study, the partial safety factors are calculated by considering the correlation between wave height and wave steepness. Smaller partial safety factors and smaller armor weight are obtained if the correlation is taken into account. The reduction becomes prominent as the probability of failure decreases (or the design armor weight increases). The correlation between wave height and steepness in real sea is also estimated by using the wave hindcasting data around the Korean Peninsula. [ABSTRACT FROM AUTHOR]

Reliability design methods have been developed for breakwater designs since the mid-1980s. The reliability design method is classified into three categories depending on the level of probabilistic concepts being employed, i.e. Level 1, 2, and 3 methods. Each method gives results in different forms, but all of them can be expressed in terms of probability of failure so that the difference can be compared among the different methods. In this study, we apply the reliability design methods to the stability of armor blocks and sliding of caissons of the breakwater of Donghae Harbor located in the east coast of Korea, which was constructed by traditional deterministic design methods to be damaged in 1987 and reinforced in 1991. Analyses are made for the breakwaters before the damage and after the reinforcement. The allowable probability of failure of a Tetrapod armor layer of 50 year's lifetime is proposed as 40% for existing stability formulas, whilst that for caisson sliding as 20% with the failure criterion for the cumulative sliding distance over the lifetime of 0.1 m. The probability of failure before the damage is much higher than the allowable value for both stability of armor blocks and sliding of caissons, indicating that the breakwater was under-designed. The probability of failure for the reinforced breakwater is lower than the allowable value, indicating that the breakwater became stable after the reinforcement. On the other hand, the results of different reliability design methods were in fairly good agreement, confirming that there is not much difference among the different methods. [ABSTRACT FROM AUTHOR]