Tunnel and Underground Space (터널과지하공간)

Korean Society for Rock Mechanics and Rock Engineering (한국암반공학회)
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Analytical Formula for the Equivalent Mohr-Coulomb Strength Parameters Best-fitting the Generalized Hoek-Brown Criterion in an Arbitrary Range of Minor Principal Stress

임의 최소주응력 구간에서 일반화된 Hoek-Brown 파괴기준식을 최적 근사하는 등가 Mohr-Coulomb 강도정수 계산식

  • Lee, Youn-Kyou (Department of Coastal Construction Engineering, Kunsan National University)
  • 이연규 (군산대학교 건축.해양건설융합공학부)
  • Received : 2019.05.22
  • Accepted : 2019.06.05
  • Published : 2019.06.30
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Abstract

The generalized Hoek-Brown (GHB) failure criterion developed by Hoek et al. (2002) is a nonlinear function which defines a stress condition at failure of rock mass. The relevant strength parameter values are systematically determined using the GSI value. Since GSI index is a value quantifying the condition of in-situ rock mass, the GHB criterion is a practical failure condition which can take into the consideration of in-situ rock mass quality. Considering that most rock mechanics engineers are familiar with the linear Mohr-Coulomb criterion and that many rock engineering softwares incorporate Mohr-Coulomb criterion, the equations for the equivalent friction angle and cohesion were also proposed along with the release of the GHB criterion. The proposed equations, however, fix the lower limit of the minor principal stress range, where the linear best-fitting is performed, with the tensile strength of the rock mass. Therefore, if the tensile stress is not expected in the domain of analysis, the calculated equivalent friction angle and cohesion based on the equations in Hoek et al. (2002) could be less accurate. In order to overcome this disadvantage of the existing equations for equivalent friction angle and cohesion, this study proposes the analytical formula which can calculate optimal equivalent friction angle and cohesion in any minor principal stress interval, and verified the accuracy of the derived formula.

Hoek et al.(2002)이 개발한 일반화된 Hoek-Brown(GHB) 파괴기준식은 암반의 파괴응력 조건을 정의하는 비선형 함수이다. 관련 강도정수들은 GSI 지수값을 이용하여 체계적으로 결정된다. GSI 지수는 현장 암반의 상태를 정량화한 수치이므로 GHB 파괴기준식은 현장의 암반조건을 파괴기준식에 반영할 수 있는 실용적인 암반파괴함수이다. 대부분의 암반공학 기술자들이 선형 Mohr-Coulomb 파괴기준식에 익숙하며, 다수의 암반공학 소프트웨어들이 Mohr-Coulomb 식을 채택하고 있음을 고려하여 등가마찰각과 등가점착력 계산식이 GHB 파괴기준식 발표와 함께 제시되었다. 그러나 이 목적으로 제시된 등 가마찰각 및 등가점착력 계산식은 선형 최적화가 수행되는 최소주응력 범위의 하한 값을 암반의 인장강도로 고정시키고 있다. 따라서 해석영역에 인장응력이 분포하지 않은 경우 Hoek et al.(2002)의 제안식을 이용한 등가마찰각 및 등가점착력 산정결과는 정확성이 떨어질 수 있다. 이러한 기존 등가마찰각 및 등가점착력 산정수식의 단점을 극복하기 위하여 이 연구에서는 임의의 최소주응력 구간에 대해서도 최적 등가마찰각과 등가점착력을 계산할 수 있는 해석적 수식을 유도하고 결과식의 정확성을 검증하였다.

Keywords

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Fig. 1. Linear approximation of GHB rock mass failure criterion by Hoek et al. (2002)

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Fig. 2. Linear best-fitting of the GHB criterion in (a) an arbitrary range of σ3 and (b) the corresponding range of the transformed stress

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Fig. 3. Circular tunnel subjected to biaxial stress field.

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Fig. 4. Equivalent M-C strength parameter values from two different approaches for varying GSI value; (a) Friction angle, (b) Cohesion

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Fig. 5. Ratios of the equivalent M-C parameter values to the equivalent values estimated by Hoek et al. (2002) for the range of compressive minor principal stress

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