Approximate Analytical Formula for Minimum Principal Stress Satisfying the Generalized Hoek-Brown Failure Criterion

Youn-Kyou Lee

doi:10.7474/TUS.2021.31.6.480

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2021 Vol.31, Issue 6 Preview Page Next Page

Original Article

Approximate Analytical Formula for Minimum Principal Stress Satisfying the Generalized Hoek-Brown Failure Criterion 일반화된 Hoek-Brown 파괴기준식을 만족하는 최소주응력의 해석적 근사식

31 December 2021. pp. 480-493

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Abstract

Since the generalized Hoek-Brown criterion (GHB) provides an efficient way of identifying its strength parameter values with the consideration of in-situ rock mass condition via Geological Strength Index (GSI), this criterion is recognized as one of the standard rock mass failure criteria in rock mechanics community. However, the nonlinear form of the GHB criterion makes its mathematical treatment inconvenient and limits the scope of its application. As an effort to overcome this disadvantage of the GHB criterion, the explicit approximate analytical equations for the minimum principal stress, which is associated with the maximum principal stress at failure, are formulated based on the Taylor polynomial approximation of the original GHB criterion. The accuracy of the derived approximate formula for the minimum principal stress is verified by comparing the resulting approximate minimum principal stress with the numerically calculated exact values. To provide an application example of the approximate formulation, the equivalent friction angle and cohesion for the expected plastic zone around a circular tunnel in a GHB rock mass are calculated by incorporating the formula for the approximate minimum principal stress. It is found that the simultaneous consideration of the values of m_i, GSI and far-field stress is important for the accurate calculation of equivalent Mohr-Coulomb parameter values of the plastic zone.

Keywords

Generalized Hoek-Brown criterion

Minimum principal stress

Taylor polynomial approximation

Friction angle

Cohesion

일반화된 Hoek-Brown(GHB) 파괴기준식은 GSI 값을 이용하여 현장 암반조건이 반영된 강도정수 값을 효과적으로 결정할 수 있기 때문에 암반공학 분야에서 표준 파괴기준식의 하나로 인식되고 있다. 그러나 GHB 파괴기준식의 비선형적 형태는 이 식의 수학적 취급을 어렵게 하고 이 식의 적용 범위를 제약하는 요인이 되고 있다. GHB 파괴기준식의 이러한 단점을 극복하기 위한 노력의 하나로 Taylor 다항함수 근사원리를 적용하여 파괴 최대주응력에 대응하는 최소주응력을 근사적으로 계산할 수 있는 명시적, 해석적 수식을 유도하였다. 근사식으로 구한 최소주응력과 수치해석적으로 계산한 정해를 비교하여 이 연구에서 유도한 최소주응력 근사식의 정확성을 검증하였다. 연구결과의 응용사례를 제시하기 위해 근사 최소주응력 계산식을 활용하여 GHB 암반에 굴착된 원형터널 주변에 예상되는 소성영역의 등가 마찰각과 등가 점착력을 계산하였다. 소성영역의 등가 Mohr-Coulomb 강도정수를 정밀하기 산정하기 위해서는 m_i, GSI, 초기지압의 크기를 동시에 고려하는 것이 중요한 것으로 나타났다.

키워드

일반화된 Hoek-Brown 파괴기준식

최소주응력

Taylor 다항함수 근사

마찰각

점착력

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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 : 31
No :6
Pages :480-493
Received Date : 2021-11-08
Revised Date : 2021-11-23
Accepted Date : 2021-11-24
DOI :https://doi.org/10.7474/TUS.2021.31.6.480

Tunnel and Underground Space ISSN:1225-1275(Print) 2287-1748(Online) 터널과 지하공간

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