비선형 Mohr 포락선을 이용한 암반사면 평면파괴 안전율 계산
Calculation of Factor of Safety for Plane Failure of Rock Slope Utilizing the Nonlinear Mohr Envelope
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일반화된 Hoek-Brown (GHB) 암반파괴기준식의 약점 중 하나는 이 식을 명시적인 Mohr 포락선식으로 변환하는 것이 어렵다는 점이다. 암반공학에서 활용되는 주요 수치해석 기법들은 파괴기준식이 Mohr 포락선 형태로 표시될 수 있을 때 활용범위가 훨씬 더 넓어진다. 이 연구에서는 Lee (2018) 의 연구를 바탕으로 암반의 전단강도를 더욱 정확하게 근사할 수 있는 GHB식의 근사 Mohr 포락선식을 제안하였고 그 정확성을 검증하였다. 제안된 Mohr 파괴포락선식을 Bishop의 간편법에 적용하여 암반사면의 평면파괴 안전율을 계산하였고, 그 결과를 Hoek et al. (2002)이 제안한 선형근사Mohr 포락선을 적용한 결과와 비교하였다. 0 < GSI < 80 범위에서는 선형근사 Mohr 포락선을 사용할 때 비선형 Mohr 포락선을 사용하는 경우보다 안전율이 과대평가 되었다.
Abstract
A weakness of the generalized Hoek–Brown (GHB) criterion is the difficulty of converting it into an explicit Mohr envelope equation. Many important numerical analysis techniques in rock engineering would have a wider scope of applications if a failure criterion in the form of a Mohr envelope is available. In this paper, based on the study of Lee (2018), an approximate Mohr envelope equation of the GHB criterion that can more accurately approximate the shear strength of the rock mass is proposed, and its accuracy is verified. The proposed Mohr envelope equation was applied to Bishop’s simplified method to calculate the factor of safety for the plane failure of a rock slope. The results were compared with those obtained by applying the linear approximate Mohr envelope of Hoek et al. (2002). In the range of 0 < GSI < 80, the factor of safety was overestimated when the linear Mohr envelope was used compared with using the nonlinear Mohr envelope.
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