• Journal of Korean Society of Coastal and Ocean Engineers
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• v.15 no.4
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• pp.249-258
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• 2003

In this study, the stability of armor blocks of rubble-mound breakwaters is investigated based on the 2-dimensional hydraulic model test with irregular waves. Amor blocks were used the three types; rock, cube and tetrapod. And Hudson formula and van der Meer formula which are used for calculating the weight of armor blocks are considered. Hudson formula was developed from regular wave tests, while van der Meer formula was developed from irregular wave tests. The purpose of this paper is to compare and test two selected stability formulas using the experimental data.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.21 no.5
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• pp.345-356
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• 2009

Tetrapod has been used as the armor blocks of most rubble mound breakwaters constructed in Korea. The Hudson formula has been widely used in the design of breakwater armor blocks in Korea. In the present study, we calculate the load and resistance partial safety factors of the Hudson formula for Tetrapod armors. The partial safety factors were calculated for the typical breakwater cross-sections of 12 trade harbors and 8 coastal harbors in Korea. The mean and standard deviation of them were also calculated. The mean values were compared with the partial safety factors of US Army (2006). The load and resistance factors are slightly smaller and larger, respectively, than the US Army values. However, the overall safety factors obtained by multiplying the load and resistance factors are close to the US Army values. The result of the present study could be used as the basic data to propose authorized partial safety factors in the future.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.15 no.3
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• pp.186-189
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• 2003

Various empirical formulas have been developed to describe the stability of breakwater armor stones. The Hudson formula is known to have needs to be refined in many ways. but it is most widely used because of its simplicity. The van der Meer formula is sometimes used for the cross-check, but it is not very popularly used due to its complexity and the uncertainty of the relevant parameters. Recently, on the other hand, Yoo(2003) proposed a formula of a simple form using a new non-dimensional number which is called 'action slope' (abbreviated as Yoo formula hereinafter). In this study, in order to provide coastal engineers with some idea of the use of these formulas, their accuracies were estimated by comparing with the experimental data reported by van der Meer in 1987 and 1988. It was found that the van der Meer formula showed the highest accuracy, while the Hudson formula of very low accuracy needed considered judgment on its use. On the other hand, the Yoo formula of slightly lower accuracy but simpler expression than the van der Meer formula seems to be able to be used in engineering practice if a slightly higher safety factor is taken.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.25 no.4
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• pp.181-190
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• 2013

In this study, a total of 51 cases of hydraulic model tests has been conducted for various wave conditions and slope angles of breakwater to develop a stability formula for Rakuna-IV armoring a rubble-mound breakwater. The stability number of the formula is expressed as a function of relative damage, number of waves, structural slope, and surf similarity parameter. The stability formula is derived separately for plunging and surging waves, the greater of which is used. The transitional surf similarity parameter from plunging waves to surging waves is also presented. Lastly, to explain the stability of Rakuna-IV to the engineers who are familiar with the stability coefficient in the Hudson formula, the required weight of Rakuna-IV is calculated for varying significant wave height for typical plunging and surging wave conditions, which is then compared with those of the Hudson formula using several different stability coefficients.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.13 no.1
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• pp.9-17
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• 2001

A probability of failure of armor units on rubbJe-mound breakwater are evaluated by using the direct method for reliability analysis, which is represented as a function of safety factor that has been extensively used in practical design. The reliability function is fonnulated based on Hudson formula suggested for designing the stable size of armor units on rubble-mound breakwater. Several kinds of stability coefficient are applied separately to calculate the probability of failure with respect to the type of armor units, breaking/nonbreaking and the correlation coefficients between random variables. [n addition, the sensitivity analyses are carried out to investigate quantitatively into the effects of each random variable in the reliability function on the probability of failure.

• Textile Coloration and Finishing
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• v.18 no.5 s.90
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• pp.72-79
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• 2006

There are many discrepancies between visually perceived color-difference and that which is quantified from an instrumental measurement when dark color samples are measured in the textile industry. The samples were prepared to represent these dark shades and the values of the instrumental results from conventional color-difference formulae(CIELAB, CMC, BFD II, CIE94, LCD99 and CIEDE2000). Those of visual assessment were compared. The experimental results show that the CIELAB formula gives the best performance over other formulae, and the CIEDE2000 formula for the color-difference according to chroma presents the worst performance. Therefore, we can say that the problems in color matching of dark shades are caused by imperfect formula, because the results obtained from a color-difference formulae are different and the CMC which is used as a standard color-difference formula in the textile industry is not correct. So, a revised color-difference formula is proposed in this study, to account for these problems.

• Textile Coloration and Finishing
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• v.18 no.5 s.90
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• pp.80-87
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• 2006

A new fastness formula based on the CIEDE2000 color-difference formula was developed by B. Rigg and his coworkers. It is much simpler to calculate the staining fastness grade than the ISO 105-A04 fastness formula based on the CIELAB color-difference formula. Sample pair sets, which cover a wide color space range were accumulated from the NCS(Natural Color System) color book. for those sample pair sets, a visual measurement experiment and an instrumental measurement experiment of fastness grade were carried out. Each performance of the ISO 105-A43 fastness formula and newly developed fastness formula was compared through degree of agreement for visual measurement results. The newly developed fastness formula indicated improved performance for measuring fastness grade as it was confirmed that the performance of the current ISO fastness formula ISO 105-A04 for assessing staining, was inadequate for measuring fastness grade. Then the fastness formulae were examined more closely according to the particular color spaces and the correlation of hue, lightness and chroma for measuring staining fastness grade was also considered to recommend more improved fastness formula. By modifying the weighting functions of CIEDE2000, which is a basis of new fastness formula developed by B. Rigg, a modified fastness formula is proposed in this study.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.24 no.2
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• pp.138-148
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• 2012

A stochastic reliability analysis model has been developed for evaluating the time-dependent stability performance of armor units of rubble-mound breakwaters subjected to the multiple loads of arbitrary magnitudes which could be occurred randomly. The initial structural capacities and the damage rates of armor units of rubble-mound breakwaters could be estimated as a function of the incident wave height with a given return period by using the modified Hudson's formula and Melby's formula. The structural stability performances of armor units of rubble-mound breakwaters could be analyzed in detail through the lifetime reliability investigations according to the limit states such as the serviceability or ultimate limit state and the conditions of multiple loads. Finally, repair intervals for the structural management of armor units of rubble-mound breakwaters could quantitatively be evaluated by a new approach suggested in this paper that has been based on the target probability for repair and the accumulated probabilities of failure obtained from the present stochastic reliability analysis model.

• Journal of Industrial Technology
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• v.28 no.B
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• pp.157-165
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• 2008

Level II AFDA and Level III MCS reliability models are applied to analyze the stability of armor units on trading and coastal harbors in Korea. Hudson's formula and Van der Meer's formula are used in this reliability analysis. Also, probability density functions of reliability index and probability of failure are derived by the additional analysis. In addition, the partial safety factors of all harbors related to armor units can be straightforwardly evaluated by the inverse-reliability method. The upper and lower limits and average level of partial safety factors can be statistically investigated with the results of all cases applied in this paper. Therefore, it may be possible to design armor units of new breakwaters including the uncertainty of random variable and target level by using the present results.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.28 no.5
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• pp.277-283
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• 2016

Tetrapod is one of the most widely used concrete armor units for rubble mound breakwaters. The calculation of the stability number of Tetrapods is necessary to determine the optimal weight of Tetrapods. Many empirical formulas have been developed to calculate the stability number of Tetrapods, from the Hudson formula in 1950s to the recent one developed by Suh and Kang. They were developed by using the regression analysis to determine the coefficients of an assumed formula using the experimental data. Recently, software engineering (or machine learning) methods are introduced as a large amount of experimental data becomes available, e.g. artificial neural network (ANN) models for rock armors. However, these methods are seldom used probably because they did not significantly improve the accuracy compared with the empirical formula and/or the engineers are not familiar with them. In this study, we propose an explicit method to calculate the stability number of Tetrapods using the weights and biases of an ANN model. This method can be used by an engineer who has basic knowledge of matrix operation without requiring knowledge of ANN, and it is more accurate than previous empirical formulas.