The Journal of Engineering Geology (지질공학)

The Korean Society of Engineering Geology (대한지질공학회)
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A Case Study on Quantifying Uncertainties of Geotechnical Random Variables

지반 확률변수의 불확실성 정량화에 관한 사례연구

  • Received : 2012.01.09
  • Accepted : 2012.03.05
  • Published : 2012.03.30
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Abstract

Probabilistic design methods have been used as a design standard in Korea and abroad for achieving reasonable design by considering the statistical uncertainties of soil properties. In this study, the following techniques for reflecting geotechnical uncertainty are analyzed: quantification of the uncertainties of geotechnical random variables, and consideration of economic feasibility in design by minimizing the uncertainties related to the number of samples. To quantify the uncertainties, the techniques were applied to soil properties obtained from samples collected and tested in the field. The results showed an underestimation of the standard deviation by the 3-sigma approach in comparison with calculations using data from the samples. This finding indicates that economical design is possible in terms of probability. However, when compared with the Bayesian approach, which does not consider the number of samples, variability in the 3-sigma approach is underestimated for some variables. This finding also indicates a safety issue, whereas the number of samples based on the Bayesian approach showed the lowest variance. The variance of the probability density function showed a marked decrease with increasing number of samples, to converge at a certain level when the number exceeds 25. Of note, the estimation of values is more reliable for random variables having low variability, such as soil unit weight, and can be obtained with a small number of samples.

지반정수의 통계적 불확실성을 설계에 반영함으로써 합리적인 설계를 하기위한 확률론적 설계법이 국내외에서 설계기준으로 채택되고 있는 추세이다. 본 연구에서는 지반 확률변수의 불확실성을 정량화 하기위한 기법과 획득한 자료의 수에 따라 불확실성을 최소화함으로써 설계의 경제성을 기할 수 있는 기법들을 분석하였다. 국내의 특정 현장에서 채취되고 실험된 토질정수를 불확실성 정량화를 위한 몇 가지 기법들에 적용하고 비교하였다. 그 결과 3-sigma기법은 자료를 이용하여 산정된 표준편차에 비하여 모두 낮게 평가되어 확률론적으로 경제적인 설계가 가능하나 샘플 수를 고려하지 않은 Bayesian 기법을 이용하여 사전정보와 조합한 경우 일부의 변수는 3-sigma기법이 작게 산정되어 불안전한 설계의 우려가 있었다. 반면, 샘플 수를 고려하여 Bayesian 분석한 경우는 상대적으로 가장 낮은 분산을 보였다. 샘플 수가 증가할수록 확률밀도함수의 분산이 현저히 감소하였고 25개 이상인 경우 전체적으로 일정수준에 수렴하였다. 특히, 단위중량과 같이 변동성이 작은 확률변수의 경우 상대적으로 적은 샘플 수에서도 사후정보에서 신뢰도 높은 값을 추정할 수 있었다.

Keywords

References

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