• 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 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.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 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.

• Journal of Industrial Technology
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• v.21 no.B
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• pp.163-174
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• 2001

A dynamic reliability model for analyzing the stability of armor units on rubble-mound breakwater is mathematically developed by using Hudson's formula and definition of single-failure mode. The probability density functions of resistance and loading functions are defined properly, the related parameters to those probability density functions are also estimated straightforwardly by the first-order analysis. It is found that probabilities of failure for the stability of armor units on rubble-mound breakwater are continuously increased as the service periods are elapsed, because of the occurrence of repeated loading of random magnitude by which the resistance may be deteriorated. In particular, the factor of safety is incorporated into the dynamic reliability model in order to evaluate the probability of failure as a function of factor of safety. It may thus be possible to take some informations for optimal design as well as managements and repairs of armor units on rubble-mound breakwater from the dynamic reliability analyses.

• 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.21 no.1
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• pp.15-29
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• 2009

Most breakwater armor blocks are designed by using Hudson's or van der Meer's formula. The minimum weight of armor blocks is calculated by equating the resistance to the load in each formula. The larger value is then chosen as the design weight. In this study, we have performed reliability analyses for thus designed breakwater armor blocks of 12 trade harbors and 8 coastal harbors in Korea. The probability of failure calculated by the reliability analysis provides a criterion for evaluating the stability of armor blocks. The calculated probability of failure was almost same for all the breakwaters so that we were able to quantitatively evaluate the safety level of armor blocks of existing breakwaters. We also found that the safety factor used in the deterministic design method and the probability of failure in the reliability design method show a linear relationship. Therefore the probability of failure of existing breakwaters can be quantitatively calculated from the safety factors. The calculated probability of failure could also be used for determining the target probability of failure in the future.

• Journal of Ocean Engineering and Technology
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• v.24 no.2
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• pp.18-24
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• 2010

Submerged rubble structures include artificial reef and the mound part of the rubble mound breakwater. Artificial reef is a type of the submerged wave absorbing structure installed in a coastal zone to prevent beach erosion and designed to initially reduce the energy of incoming waves so that its run-up height and overtopping quantity can be decreased. In order to ascertain the stability of such submerged rubble structures, minimum weight of the rubble has to be calculated first from the incoming wave height using Hudson's formula or Brebner-Donnelly formula. Based on the calculated minimum weight, a model is built for use in a hydraulic model test carried out to check its stability. The foregoing two formulas used to calculate the minimum weight are empirically derived formulas based on the result of the tests on the rubble mound breakwater and it is, therefore, difficult for us to apply them directly in the calculation of the minimum weight of the submerged structures. Accordingly, this study comes up with a numerical simulation method capable of deformation analysis for rubble structures. This study also tries to identify the deformation mechanism of the submerged rubble structures using the numerical simulation. The method researched through this study will be sufficient for use for usual preparations of the design guidelines for submerged rubble structures.

• 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.