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수치해석과 연계한 지하구조물의 확률론적 신뢰성 평가를 위한 점추정법의 적용성에 관한 비교 연구

Comparative Study on the Applicability of Point Estimate Methods in Combination with Numerical Analysis for the Probabilistic Reliability Assessment of Underground Structures

  • 박도현 (한국지질자원연구원 지구환경연구본부) ;
  • 김형목 (한국지질자원연구원 지구환경연구본부) ;
  • 류동우 (한국지질자원연구원 지구환경연구본부) ;
  • 최병희 (한국지질자원연구원 지구환경연구본부) ;
  • 한공창 (한국지질자원연구원 지구환경연구본부)
  • 투고 : 2012.03.12
  • 심사 : 2012.03.30
  • 발행 : 2012.04.30

초록

점추정법은 exact probabilistic method로 간주되는 Monte Carlo simulation에 비해 계산의 정확도는 다소 떨어지지만, 성능함수의 통계 모멘트를 분석하기 위한 샘플링 수를 크게 줄일 수 있는 해석 과정에서의 간편함과 비교적 정확한 통계 모멘트의 계산으로 인해 지반 및 암반공학에서의 확률론적 신뢰성 평가에 자주 사용되고 있다. 본 연구에서는 Rosenblueth와 Zhou & Nowak의 점추정법과 Monte Carlo simulation의 계산 결과를 비교 분석하여 점추정법의 정확도와 적용성을 조사하였다. 비교 분석은 해석적 해가 주어진 탄성 지반내 원형터널의 라이닝 지보 문제를 대상으로 하였다. 분석 결과, 해석적 해가 비선형 함수임에도 불구하고, 점추정법과 Monte Carlo simulation에 의해 계산된 통계 모멘트가 평균 약 1-2%의 오차를 보여 수치해석과 연계한 지하구조물의 확률론적 신뢰성 평가를 위한 점추정법의 적용성을 확인하였다.

Point estimate method has a less accuracy than Monte Carlo simulation that is usually considered as an exact probabilistic method, but this method still remains popular in probability-based reliability assessment in geotechnical and rock engineering, because it significantly reduce the number of sampling points and produces the statistical moments of a performance function in a reasonable accuracy. In the present study, we investigated the accuracy and applicability of point estimate methods proposed by Rosenblueth and Zhou & Nowak by comparing the results of these two methods with those of Monte Carlo simulations. The comparison was carried out for the problem of a lined circular tunnel in an elastic medium where an closed-form analytical solution is given. The comparison results showed that despite the non-linearity of the analytical solution, the statistical moments calculated by the point estimate methods and the Monte Carlo simulations agreed well with an average error of roughly 1-2%. This average error demonstrates the applicability of the two point estimate methods for the probabilistic reliability assessment of underground structures in combination with numerical analysis.

키워드

참고문헌

  1. Dohyun Park, Eui-Seob Park, Won-Kyong Song, Dong-Woo Ryu, 2010, Reliability Assessment of Tunnel Support Systems Using a Probability-Based Method. Korean Society for Rock Mech., Tunnel and Underground Space, 20.1, 39-48.
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피인용 문헌

  1. Analysis of the Optimal Separation Distance between Multiple Thermal Energy Storage (TES) Caverns Based on Probabilistic Analysis vol.24, pp.2, 2014, https://doi.org/10.7474/TUS.2014.24.2.155