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Original Article

Approximate Shear Strength Formula Implied in the Generalized Hoek-Brown Failure Criterion

일반화된 Hoek-Brown 파괴조건식에 내포된 전단강도 근사식

Youn-Kyou Lee1*
이 연규1*
1Department of Coastal Construction Engineering, Kunsan National University
1군산대학교 건축·해양건설융합공학부
* Corresponding Author
31 October 2018. pp. 426-441
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Abstract

Recently, the generalized Hoek-Brown (GHB) failure criterion has been actively employed in various rock engineering calculations, but the analytical form of the corresponding Mohr failure envelope is not available, making it difficult to extend the application of the GHB criterion. In order to overcome this disadvantage, this study proposes a new method to express the tangential friction angle as an explicit function of normal stress by invoking the polynomial best-fitting to the relationship between normal stress and tangent friction angle implied in the GHB failure function. If this normal stress - tangential friction angle relationship is best-fitted with linear or quadratic polynomial function, it is possible to find the analytical root for tangential friction angle. Subsequently, incorporating the root into the relationship between shear stress and tangential friction angle accomplishes the derivation of the approximate Mohr envelope for the GHB criterion. It is demonstrated that the derived approximate Mohr failure envelopes are very accurate in the entire range of GSI value.

Keywords
Generalized Hoek-Brown criterion
Mohr envelope
Tangential friction angle
Tangential cohesion
Linear and quadratic best-fitting of curve

일반화된 Hoek-Brown (GHB) 파괴조건식은 최근 각종 암반공학적 계산에 활발히 이용되고 있지만 Mohr 파괴포락선이 해석적 수식으로 표시되지 않아 적용범위를 넓히는데 어려움이 있다. 이러한 단점을 극복하기 위해 이 연구에서는 GHB 파괴함수에 내포된 수직응력 - 접선마찰각 관계식을 다항식으로 최적 근사시켜 접선마찰각을 수직응력의 명시적 근사함수로 표시하는 새로운 방법을 제안하였다. 이 수직응력 - 접선마찰각 관계식을 직선 또는 2차 다항식으로 최적 근사시킬 경우 접선마찰각에 대한 해석적 해가 존재한다. 이 해를 전단응력 - 접선마찰각 관계식에 대입하면 GHB 파괴함수의 근사적 Mohr 파괴포락선을 유도하는 것이 가능하다. 유도한 근사 Mohr 파괴포락선은 GSI 값 전체 범위에서 정해와 매우 근사함이 입증되었다.

키워드
일반화된 Hoek-Brown 파괴조건식
Mohr 포락선
접선마찰각
접선점착력
곡선의 직선함수 및 이차함수 최적근사
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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 : 28
  • No :5
  • Pages :426-441
  • Received Date : 2018-09-10
  • Revised Date : 2018-10-01
  • Accepted Date : 2018-10-01
  • DOI :https://doi.org/10.7474/TUS.2018.28.5.426
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