• Journal of Korean Society of Coastal and Ocean Engineers
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• v.15 no.2
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• pp.86-96
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• 2003

A fracture or breakage of the concrete armor units in the primary cover layer of breakwaters is studied by using the reliability analysis which may be defined as the structural stability. The reliability function can be derived as a function of the angle of rotation that represents the rocking of armor units quantitatively. The relative influences of all of random variables related to the material and geometric properties on the fracture of armor units is analyzed in detail. In addition, the probability of failure for the fracture of individual armor unit can be evaluated as a function of the incident wave height. Finally, Bernoulli random process and the allowable fracture ratio may be introduced together in this paper, by which the probability of failure of a breakwater due to the fracture of armer units can be obtained straightforwardly. It is found that the probability of failure of a breakwater due to the fracture of armor units may be varied with the several allowable fracture ratios. Therefore, it should be necessary to consider the structural stability as well as the hydraulic stability for the design of breakwaters with multi-leg slender concrete armor units of large size under wave action in deep water.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.16 no.3
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• pp.142-151
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• 2004

A method for the determination of concrete armor unit weights with hydraulic stability and structural stability may be formulated in this paper. The hydraulic stability is analyzed by using Hudson's formula, the structural stability is also studied by evaluation of maximum flexural tensile stresses in armor unit induced by the impact loads and by comparison of those with the tensile resistance strength directly. The applicable criteria for concrete armor units can be represented as a function of design wave heights with return period, armor weights, and tensile strengths for the practical uses. In addition, reliability analyses for two failure modes are carried out to take into account some uncertainties. Finally, a series system for two-failure mode analysis can be made up straightforwardly, by which the optimal weights of armor units can be estimated with the various relative breakages, given the specific target probability of failure under the concepts of reliability-based design method.

• 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.20 no.1
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• pp.42-48
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• 2008

A system of risk assessment is developed by using the reliability analysis which evaluate quantitatively both stability and performance of sloped-coastal structures according to several scenarios of sea-level rise. By using reliability functions on armor unit and run-up, the probabilities of failure can be straightforwardly calculated with respect to several design parameters such as nominal diameter of armor unit, slope of coastal structure, and freeboard height. By comparing the results before and after sea-level rise, it may be possible to exactly assess some ranges of decrease of stability and performance of sloped-coastal structure with respect to sea-level rise. Therefore, it can also be possible to make a decision which parameters should be repaired or strengthened in order to maintain the original stability and performance of sloped-coastal structures. Finally, The present results may be useful for designing some kinds of new sloped-coastal structures including the effect of sea-level rise.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.29 no.2
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• pp.109-120
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• 2017

A discounted cost model for preventive maintenance of armor units of rubble-mound breakwaters is mathematically derived by combining the deterioration model based on a discrete-time stochastic process of shock occurrence with the cost model of renewal process together. The discounted cost model of condition-based maintenance proposed in this paper can take into account the nonlinearity of cumulative damage process as well as the discounting effect of cost. By comparing the present results with the previous other results, the verification is carried out satisfactorily. In addition, it is known from the sensitivity analysis on variables related to the model that the more often preventive maintenance should be implemented, the more crucial the level of importance of system is. However, the tendency is shown in reverse as the interest rate is increased. Meanwhile, the present model has been applied to the armor units of rubble-mound breakwaters. The parameters of damage intensity function have been estimated through the time-dependent prediction of the expected cumulative damage level obtained from the sample path method. In particular, it is confirmed that the shock occurrences can be considered to be a discrete-time stochastic process by investigating the effects of uncertainty of the shock occurrences on the expected cumulative damage level with homogeneous Poisson process and doubly stochastic Poisson process that are the continuous-time stochastic processes. It can be also seen that the stochastic process of cumulative damage would depend directly on the design conditions, thus the preventive maintenance would be varied due to those. Finally, the optimal periods and scale for the preventive maintenance of armor units of rubble-mound breakwaters can be quantitatively determined with the failure limits, the levels of importance of structure, and the interest rates.

• Journal of the Korea Concrete Institute
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• v.16 no.5 s.83
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• pp.659-666
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• 2004

In this study, for the establishment of the performance evaluation methods and the quality control standard of durability recovery method, the quantitative exposure data by long term exposure test under the coast and air environment is accumulated and analyzed. Investigating and evaluating the result of exposure test during 18 months of exposure age under the coastal and normal atmosphere environment, micro crack, swelling and spatting of surface coating material crack of repair standards of repair material and method through continuous exposure test in the future.