• Journal of Korean Society of Coastal and Ocean Engineers
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• v.13 no.4
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• pp.319-326
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• 2001

This paper reports on a recent investigation to determine criteria for the design of rubble-mound breakwaters. Existing theories and empirica] equations have been carefully reviewed and a new relation is proposed for the determination of optimum weight of armor unit of rubble-mound breakwater. A new parameter is introduced into the new semi-theoretical equation, which is closely related with the surface particle velocity of wave motion. The laboratory data reported by van der Meer(1987) were used for the determination of proper relations of empiricat parameters introduced into the new empirical equation.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.25 no.2
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• pp.52-62
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• 2013

A stochastic Markov process (MP) model has been developed for evaluating the probability of failure of the armor unit of rubble-mound breakwaters as a function of time. The mathematical MP model could have been formulated by combining the counting process or renewal process (CP/RP) on the load occurrences with the damage process (DP) on the cumulative damage events, and applied to the armor units of rubble-mound breakwaters. Transition probabilities have been estimated by Monte-Carlo simulation (MCS) technique with the definition of damage level of armor units, and very well satisfies some conditions constrained in the probabilistic and physical views. The probabilities of failure have been also compared and investigated in process of time which have been calculated according to the variations of return period and safety factor being the important variables related to design of armor units of rubble-mound breakwater. In particular, it can be quantitatively found how the prior damage levels can effect on the sequent probabilities of failure. Finally, two types of methodology have been in this study proposed to evaluate straightforwardly the repair times which are indispensable to the maintenance of armor units of rubble-mound breakwaters and shown several simulation results including the cost analyses.

• Proceedings of the Korean Society of Coastal and Ocean Engineers Conference
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• 2003.08a
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• pp.290-293
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• 2003

경사형 방파제(rubble-mound breakwater) 설계시 제체의 장갑층으로 포설하는 블록의 규모 산정이 가장 중요한 항목인데, 경사제에서 파의 작용을 직접 받는 표층을 형성하는 개체의 중량 산정에 관하여는 오래 전부터 여러 공학자의 의해 연구되어 왔다. 대표적인 산정식들로서 barren식, Hudson식 Van der Meer식 등이 있으며, 최근 유동훈 등(2001)과 Yoo, et al.(2001)은 형태가 단순하면서도 정밀도가 높은 새로운 산정식을 개발하였다. (중략)

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.29 no.6
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• pp.389-398
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• 2017

The re-analysis on the stable weight of the concrete armor unit (CAU) at the roundhead and the suggestion of the covering range at the roundhead with the increased weight of CAU were conducted. Tetrapods were applied to the tests and the three dimensional hydraulic tests were performed. The test results for the stable weight at the roundhead area were similar to the guides from Korean Design Standard for Harbour and Fishery Port (MOF, 2014) and Coastal Engineering Manual (USACE, 2005). The investigation of covering range at the roundhead of rubble mound structures armoured with Tetrapods was suggested that the length of five times of the design wave height from the tip of the superstructure was needed and appropriate. Both sides of the superstructure should be covered with increasing weighted CAU to satisfy the stability at roundhead area.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.35 no.2
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• pp.23-32
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• 2023

Probabilistic and deterministic analyses are implemented for the armor units of rubble foundation mound of composite breakwaters which is needed to protect the upright section against the scour of foundation mounds. By a little modification and incorporation of the previous empirical formulas that has commonly been applied to design the armor units of foundation mound, a new type formula of stability number has been suggested which is capable of taking into account slopes of foundation mounds, damage ratios of armor units, and incident wave numbers. The new proposed formula becomes mathematically identical with the previous empirical formula under the same conditions used in the developing process. Deterministic design have first been carried out to evaluate the minimum weights of armor units for several conditions associated with a typical section of composite breakwater. When the slopes of foundation mound become steepening and the incident wave numbers are increasing, the bigger armor units more than those from the previous empirical formula should be required. The opposite trends however are shown if the damage ratios is much more allowed. Meanwhile, the reliability analysis, which is one of probabilistic models, has been performed in order to quantitatively verify how the armor unit resulted from the deterministic design is stable. It has been confirmed that 1.2% of annual encounter probability of failure has been evaluated under the condition of 1% damage ratio of armor units for the design wave of 50 years return period. By additionally calculating the influence factors of the related random variables on the failure probability due to those uncertainties, it has been found that Hudson's stability coefficient, significant wave height, and water depth above foundation mound have sequentially been given the impacts on failure regardless of the incident wave angles. Finally, sensitivity analysis has been interpreted with respect to the variations of random variables which are implicitly involved in the formula of stability number for armor units of foundation mound. Then, the probability of failure have been rapidly decreased as the water depth above foundation mound are deepening. However, it has been shown that the probability of failure have been increased according as the berm width of foundation mound are widening and wave periods become shortening.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.31 no.3
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• pp.158-169
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• 2019

A probabilistic model that can predict the residual useful lifetime of structure is formulated by using the gamma process which is one of the stochastic processes. The formulated stochastic model can take into account both the sampling uncertainty associated with damages measured up to now and the temporal uncertainty of cumulative damage over time. A method estimating several parameters of stochastic model is additionally proposed by introducing of the least square method and the method of moments, so that the age of a structure, the operational environment, and the evolution of damage with time can be considered. Some features related to the residual useful lifetime are firstly investigated into through the sensitivity analysis on parameters under a simple setting of single damage data measured at the current age. The stochastic model are then applied to the rubble-mound breakwater straightforwardly. The parameters of gamma process can be estimated for several experimental data on the damage processes of armor rocks of rubble-mound breakwater. The expected damage levels over time, which are numerically simulated with the estimated parameters, are in very good agreement with those from the flume testing. It has been found from various numerical calculations that the probabilities exceeding the failure limit are converged to the constraint that the model must be satisfied after lasting for a long time from now. Meanwhile, the expected residual useful lifetimes evaluated from the failure probabilities are seen to be different with respect to the behavior of damage history. As the coefficient of variation of cumulative damage is becoming large, in particular, it has been shown that the expected residual useful lifetimes have significant discrepancies from those of the deterministic regression model. This is mainly due to the effect of sampling and temporal uncertainties associated with damage, by which the first time to failure tends to be widely distributed. Therefore, the stochastic model presented in this paper for predicting the residual useful lifetime of structure can properly implement the probabilistic assessment on current damage state of structure as well as take account of the temporal uncertainty of future cumulative damage.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.23 no.1
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• pp.109-117
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• 2011

It was calculated using empirical formulas for the weight of Tetrapod, which was a representative armor unit in the rubble mound breakwater in Korea. As the formulas were evaluated from a curve-fitting with the result of hydraulic test, the uncertainty of experimental error was included. Therefore, the neural network and M5' model tree were used to minimize the uncertainty and predicted the stability number of armor block. The index of agreement between the predicted and measured stability number was calculated to assess the degree of uncertainty for each model. While the neural network with the highest index of agreement have an excellent prediction capability, a significant disadvantage exists that general designers can not easily handle the method. However, although M5' model tree has a lower prediction capability than the neural network, the model tree is easily used by the designers because it has a good prediction capability compared with the existing empirical formula and can be used to propose the formulas like an empirical formula.