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2024 Vol.34, Issue 4 Preview Page

Original Article

Improving the Accuracy of the Mohr Failure Envelope Approximating the Generalized Hoek-Brown Failure Criterion

일반화된 Hoek-Brown 파괴기준식의 근사 Mohr 파괴포락선 정확도 개선

Youn-Kyou Lee1*
이 연규1*
1Professor, Department of Coastal Construction Engineering, Kunsan National University
1국립군산대학교 해양건설공학과 교수
*Corresponding Author
31 August 2024. pp. 355-373
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Abstract

The Generalized Hoek-Brown (GHB) criterion is a nonlinear failure criterion specialized for rock engineering applications and has recently seen increased usage. However, the GHB criterion expresses the relationship between minimum and maximum principal stresses at failure, and when GSI≠100, it has disadvantage of being difficult to express as an explicit relationship between the normal and shear stresses acting on the failure plane, i.e., as a Mohr failure envelope. This disadvantage makes it challenging to apply the GHB criterion in numerical analysis techniques such as limit equilibrium analysis, upper-bound limit analysis, and the critical plane approach. Consequently, recent studies have attempted to express the GHB Mohr failure envelope as an approximate analytical formula, and there is still a need for continued interest in related research. This study presents improved formulations for the approximate GHB Mohr failure envelope, offering higher accuracy in predicting shear strength compared to existing formulas. The improved formulation process employs a method to enhance the approximation accuracy of the tangential friction angle and utilizes the tangent line equation of the nonlinear GHB failure envelope to improve the accuracy of shear strength approximation. In the latter part of this paper, the advantages and limitations of the proposed approximate GHB failure envelopes in terms of shear strength prediction accuracy and calculation time are discussed.

Keywords
Mohr failure envelope
Hoek-Brown criterion
Shear strength
Tangential friction angle
Taylor approximation

일반화된 Hoek-Brown (GHB) 식은 암반공학적 활용에 특화된 비선형 파괴기준식이며 최근 활용 빈도가 증가하고 있다. 그러나 GHB 식은 파괴 시점의 최소주응력과 최대주응력의 관계식이며 GSI≠100이면 파괴면에 작용하는 수직응력과 전단응력의 명시적 관계식 즉, Mohr 파괴포락선식으로 표현이 어렵다는 단점을 가지고 있다. 이 단점으로 인해 GHB 식을 한계평형해석, 상계한계해석, 임계평면법 등과 같은 수치해석기법에 적용하는 것이 쉽지 않다. 이에 따라 최근 GHB Mohr 파괴포락선을 근사적인 해석식으로 표현하려는 연구가 시도되고 있으며 관련 연구에 대한 지속적 관심이 여전히 필요하다. 이 연구에서는 기존 식보다 전단강도 예측 정확도가 높은 근사 GHB Mohr 파괴포락선 수식화 방법을 제시하였다. 개선된 수식화 과정에서는 접선마찰각의 근사 정확도를 높이는 방법과 비선형 GHB 파괴포락선의 접선식을 활용하여 전단강도 근사값의 정확도를 높이는 방법이 이용되었다. 이 논문의 후반부에서는 전단강도 예측 정확성과 계산시간 측면에서 제안된 근사 GHB 파괴포락선들의 장단점을 논의하였다.

키워드
Mohr 파괴포락선
Hoek-Brown 파괴기준식
전단강도
접선마찰각
Taylor 근사
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Information
  • Publisher :Korean Society for Rock Mechanics and Rock Engineering
  • Publisher(Ko) :한국암반공학회
  • Journal Title :Tunnel and Underground Space
  • Journal Title(Ko) :터널과 지하공간
  • Volume : 34
  • No :4
  • Pages :355-373
  • Received Date : 2024-07-30
  • Revised Date : 2024-08-13
  • Accepted Date : 2024-08-14
  • DOI :https://doi.org/10.7474/TUS.2024.34.4.355
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