Journal of Korean Society of Coastal and Ocean Engineers (한국해안·해양공학회논문집)

Korean Society of Coastal and Ocean Engineers (한국해안·해양공학회)
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Reliability Analysis on Stability of Armor Units for Foundation Mound of Composite Breakwaters

혼성제 기초 마운드의 피복재 안정성에 대한 신뢰성 해석

  • Cheol-Eung Lee (Department of Architectural, Civil, and Environmental Engineering, Kangwon National University)
  • 이철응 (강원대학교 건축.토목.환경공학부)
  • Received : 2023.03.21
  • Accepted : 2023.04.12
  • Published : 2023.04.30
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Abstract

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.

혼성제 사석 기초 마운드 상에 거치되는 피복재의 소요중량을 산정하기 위한 결정론적 해석과 더불어 신뢰성 해석을 수행하였다. 사석 기초 마운드 경사, 피해율 그리고 입사파수를 고려할 수 있도록 안정수 산정을 위한 기존의 경험식을 수정하였다. 수정된 산정식은 기존 경험식을 개발하는 과정에 사용했던 것과 동일 조건에서 수학적으로 일치한다. 먼저 결정론적 설계법으로 임의의 대표단면에 대하여 여러 가지 조건을 변화시키면서 사석 기초 마운드 보호에 필요한 피복재의 소요중량을 산정하였다. 사석 기초 마운드 경사가 급할수록, 입사파수가 증가할수록 기존의 경험식으로 부터 산정된 피복재의 소요 중량보다 더 큰 피복재의 소요중량이 필요함을 확인하였다. 그러나 허용 피해율을 크게 부여하면 반대 경향이 나타난다. 한편, 본 연구에서 처음으로 사석 기초 마운드 피복재에 대한 신뢰성 해석이 수행되었는데, 이는 결정론적 설계법으로 산정된 피복재가 얼마나 안정한지를 정량적으로 확인하고, 파괴에 미치는 각 확률변수들의 불확실성에 따른 영향의 정도를 살펴보기 위함이다. 신뢰성 해석 결과에 의하면 기존 경험식이 만족하는 조건에서 산정된 피복재의 소요중량은 재현기간 50년 설계파 조건에서 단위 년에 1%의 피해가 발생할 확률 1.2%를 갖는다. 또한 영향계수 산정 결과에 의하면 입사각에 따라 약간 다르지만 전반적으로 안정계수, 파고 그리고 사석 기초 마운드상의 수심 순으로 파괴에 미치는 영향이 큼을 확인할 수 있었다. 마지막으로 안정수 산정식에 음함수적으로 포함되어 그 영향이 쉽게 확인되지 않는 확률변수의 변화에 따른 민감도 분석이 수행되었다. 해석 결과에 의하면 사석 기초 마운드의 수심이 깊어 질수록 파괴확률이 급격하게 감소하였다. 그러나 반대로 사석 기초 마운드의 폭이 커질수록, 입사 파랑의 주기가 짧을수록 파괴확률은 커지는 것으로 확인되었다.

Keywords

References

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