Narrow Results

An analytical model has been developed that can predict the scattering of irregular waves normally incident upon an array of vertical cylinders. To examine the predictability of the developed model, laboratory experiments have been made for the reflection and transmission of irregular waves from arrays of circular cylinders with various diameters and gap widths. Though the overall agreement between measurement and calculation is fairly good, the model tends to over- and under-predict the reflection and transmission coefficients, respectively, as the gap width decreases. The model also underestimates the energy loss coefficients for small gap widths because it neglects the evanescent waves near the cylinders. The peaks of the measured spectra of the reflected and transmitted waves slightly shift towards higher frequencies compared with that of the incident wave spectrum probably because of the generation of shorter period waves due to the interference of the cylinders. Both model and experimental data show that the wave reflection and transmission become larger and smaller, respectively, as the wave steepness increases, which is a desirable feature of the cylinder breakwaters.

Recently, Hanzawa et al. developed a reliability design method for the calculation of the expected damage level of armor blocks of a horizontally composite breakwater. In their method, the wave transformation from deepwater to the design site was calculated by assuming unidirectional random waves being normally incident to a straight coast with parallel depth contours. In real situations, however, directional random waves with variable principal wave directions will be incident to the shore of irregular bathymetry. In the present study, the reliability design method of Hanzawa et al. was extended to take into account the variability in wave direction in the computation of wave transformation. The directional variability includes directional spreading of waves, obliquity of the design principal wave direction from the shore-normal direction, and its variation about the design value. Even though the wave incident angle to the breakwater could be calculated, normal incidence was assumed in the calculation of the damage level of armor blocks. It was found that the inclusion of directional variability in the computation of wave transformation had great influence on the computed expected damage level of armor blocks. The previous design, which disregarded wave directionality, could either overestimate or underestimate the expected damage level by a factor of two, depending on water depth and seabed slope.

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.

Runup level exceeded by 2% of the incident waves is a key parameter in rough rock armored slopes design. From the literature survey, it is seen that the two most important factors influencing runup phenomena on rock armored slopes are structure permeability (SP) and surf similarity parameter (SSP). Since the relationships between wave runup and these parameters are complex, vague and uncertain in nature, it is quite difficult to adequately examine wave runup by conventional regressional approaches. Here, an attempt is made to construct various Takagi-Sugeno [TS, 1985] fuzzy models for predicting the 2% wave runup on rock armored slopes. The developed TS fuzzy model with two inputs namely SP and SSP yielded the best result out of all constructed models and is proposed in this study. The presented model is validated by comparison with widely used empirical model of Meer and Stam [MS, 1992], recommended by the U.S. Army Corps of Engineers [2002], using the experimental data-sets of MS. The verification process is obtained through scatter diagrams and two numerical error criterias. It was found that the TS model produce better accuracy in performance than the MS's empirical model.

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.

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.

There is limited information on wave forces on caisson breakwaters with circular caissons. In this paper we report from model tests on wave forces from regular waves on a composite breakwater with circular caissons in 55 m water depth. The results are compared with the Goda formula for wave forces on plain vertical wall caissons. The measured forces are approximately 20% lower than the results of the Goda formula for the ultimate limit state high waves (H = 16 m) and 25% for the accident limit state (H = 19.8 m). However, there have been some discussions on the accuracy of the Goda formula, from no over-prediction to approximately 10% over-prediction. Taking an over-prediction of 10% into account our results still indicate a 10%–15% force reduction for high waves by using vertical circular caissons instead of plain wall vertical caissons.

A numerical model of nearshore waves and wave-induced currents was developed to predict the wave and current fields in the vicinity of coastal structures. The wave model EBED (Mase, 2001) was modified in order to improve simulation of the wave conditions in the surf zone. The surface roller was modeled following the approaches by Dally and Brown (1995) and Larson and Kraus (2002). The wave-induced current and water level were determined from the depth-averaged momentum equations and the continuity equation. Model validation was based on high-quality data sets from experiments with structures in the Large-Scale Sediment Transport Facility (LSTF) basin of the Coastal and Hydraulics Laboratory (CHL), U.S. The computational results showed that the model can produce good agreement with the measurements for nearshore waves and currents.

The response of composite caisson breakwaters against a partial failure of the armour layer is not well understood at present. Observations in the field have indicated that higher levels of damage can be observed in the caisson, and to try to understand the mechanisms at work laboratory experiments were carried out on a range of regular waves (including breaking waves) and solitary waves (to simulate tsunami type waves). The results show how for partially failed armour layers when a high energy wave acts directly onto the caisson much higher pressures can be expected than for when a full armour layer is present. Analysis of video recordings show how the wave changes shape by "piling-up" on top of the failed armour, and as a result their destructive potential is substantially increased.