[논문]횡등방성 암석에서 겉보기 탄성정수의 방향성 변화와 탄성정수 제약조건

이연규

doi:10.7474/tus.2023.33.3.150

횡등방성 암석에서 겉보기 탄성정수의 방향성 변화와 탄성정수 제약조건
Directional Variation of Apparent Elastic Constants and Associated Constraints on Elastic Constants in Transversely Isotropic Rocks 원문보기

터널과 지하공간: 한국암반공학회지 = Tunnel and underground space, v.33 no.3, 2023년, pp.150 - 168

초록
AI-Helper

암석의 이방성 거동은 조암광물들의 방향성 배열과 미세균열의 분포 특성이 주된 원인이다. 특히, 퇴적암과 변성암은 횡등방성 강도 및 변형 특성을 또렷이 나타내는 경우가 많다. 그러므로 암석역학적 설계과정에서는 횡등방성 암석의 변형 및 파괴 특성을 정확하게 이해하는 것이 중요하다. 횡등방성 암석의 변형은 실내시험을 통해 측정할 수 있는 5개의 독립된 탄성정수를 이용하여 기술된다. 이 연구에서는 문헌에 보고된 실험자료를 이용하여 횡등방성 암석의 겉보기 탄성정수의 방향성 변화 특성을 분석하였다. 임의 방향으로 회전된 직각좌표계에서 겉보기 탄성정수 값을 효율적이고 체계적으로 계산하기 위해 Mehrabadi & Cowin의 구성방정식을 도입하였다. 문헌에 보고된 4개 횡등방성 암석을 선택하여 연약면의 방향 변화가 겉보기 탄성계수, 겉보기 전단 탄성계수, 겉보기 포아송비의 변화에 미치는 영향을 분석하였다. 이러한 분석 결과를 바탕으로 새로운 탄성정수 제약 조건식을 제안하였다. 제안한 제약 조건식을 만족하면 횡등방성 암석에서 겉보기 탄성정수의 방향성 변화는 직관적으로 예측되는 경향과 일치하게 된다.

Abstract ▼ AI-Helper

The anisotropic behavior of rocks is primarily attributed to the directional arrangement of rock-forming minerals and the distribution characteristics of microcracks. Notably, sedimentary and metamorphic rocks often exhibit distinct transverse isotropy in terms of their strength and deformation characteristics. Consequently, it is crucial to gain accurate insights into the deformation and failure characteristics of transversely isotropic rocks during rock mechanics design processes. The deformation of such rocks is described by five independent elastic constants, which are determined through laboratory testing. In this study, the characteristics of the directional variation of apparent elastic constants in transversely isotropic rocks were investigated using experimental data reported in the literature. To achieve this, the constitutive equation proposed by Mehrabadi & Cowin was introduced to calculate the apparent elastic constants more efficiently and systematically in a rotated Cartesian coordinate system. Four transversely isotropic rock types from the literature were selected, and the influence of changes in the orientation of the weak plane on the variations of the apparent elastic modulus, apparent shear modulus, and apparent Poisson's ratio was analyzed. Based on the investigation, a new constraint on the elastic constants has been proposed. If the proposed constraint is satisfied, the directional variation of the apparent elastic constants in transversely isotropic rocks aligns with intuitive predictions of their tendencies.

주제어

표/그림 (13)

그림 Fig. 1. Definition of global coordinate system for transversely isotropic rock sample
$Fig. 2. Local coordinate systems for inclined transversely isotropic rock samples: (a) rotated by an angle 𝛿 about x3 -axis and then (b)rotated by an angle 𝜃 about <TEX>$\tilde{x}_2$</TEX>-axis$ 그림 Fig. 2. Local coordinate systems for inclined transversely isotropic rock samples: (a) rotated by an angle 𝛿 about x₃ -axis and then (b)rotated by an angle 𝜃 about $\tilde{x}_2$-axis
$Fig. 3. Variations of apparent elastic modulus <TEX>$\tilde{E}_2$</TEX> in the rock samples with respect to changes in the dip angle δ of the weak planes: (a) Asan gneiss (Cho et al., 2012), (b) Taiwan marble, (c) Olkiluoto mica gneiss, and (d) O Barco de Valdeorras slate$ 그림 Fig. 3. Variations of apparent elastic modulus $\tilde{E}_2$ in the rock samples with respect to changes in the dip angle δ of the weak planes: (a) Asan gneiss (Cho et al., 2012), (b) Taiwan marble, (c) Olkiluoto mica gneiss, and (d) O Barco de Valdeorras slate
표 Table 1. Elastic constants of transversely isotropic rocks
$Fig. 4. Variation of apparent elastic modulus <TEX>$\tilde{E}_2$</TEX> in the Asan gneiss sample with respect to change in the dip angle 𝛿 of the weak plane. The elastic constants shown in the figure are cited from Yim et al.(2022)$ 그림 Fig. 4. Variation of apparent elastic modulus $\tilde{E}_2$ in the Asan gneiss sample with respect to change in the dip angle 𝛿 of the weak plane. The elastic constants shown in the figure are cited from Yim et al.(2022)
$Fig. 5. Minimum value of apparent elastic modulus <TEX>$\tilde{E}_2$</TEX> at the dip angle 𝛿=𝛿* (0° < 𝛿* < 90°) of the weak plane$ 그림 Fig. 5. Minimum value of apparent elastic modulus $\tilde{E}_2$ at the dip angle 𝛿=𝛿^* (0° < 𝛿^* < 90°) of the weak plane
$Fig. 6. Variations of apparent elastic modulus <TEX>$\tilde{E}_1$</TEX> in the rock samples with respect to changes in the orientation of the weak planes: (a) Asan gneiss (Cho et al., 2012), (b) Taiwan marble, (c) Olkiluoto mica gneiss, and (d) O Barco de Valdeorras slate$ 그림 Fig. 6. Variations of apparent elastic modulus $\tilde{E}_1$ in the rock samples with respect to changes in the orientation of the weak planes: (a) Asan gneiss (Cho et al., 2012), (b) Taiwan marble, (c) Olkiluoto mica gneiss, and (d) O Barco de Valdeorras slate
$Fig. 6. Variations of apparent elastic modulus <TEX>$\tilde{E}_{1}$</TEX> in the rock samples with respect to changes in the orientation of the weak planes: (a) Asan gneiss (Cho et al., 2012), (b) Taiwan marble, (c) Olkiluoto mica gneiss, and (d) O Barco de Valdeorras slate (continued)$ 그림 Fig. 6. Variations of apparent elastic modulus $\tilde{E}_{1}$ in the rock samples with respect to changes in the orientation of the weak planes: (a) Asan gneiss (Cho et al., 2012), (b) Taiwan marble, (c) Olkiluoto mica gneiss, and (d) O Barco de Valdeorras slate (continued)
$Fig. 7. Variations of apparent elastic shear moduli (a) <TEX>$\tilde{G}_{12}$</TEX> and (b) <TEX>$\tilde{G}_{31}$</TEX> in the Asan gneiss sample (Cho et al., 2012) with respect to changes in the orientation of the weak planes$ 그림 Fig. 7. Variations of apparent elastic shear moduli (a) $\tilde{G}_{12}$ and (b) $\tilde{G}_{31}$ in the Asan gneiss sample (Cho et al., 2012) with respect to changes in the orientation of the weak planes
$Fig. 8. Variations of apparent elastic shear modulus <TEX>$\tilde{G}_{12}$</TEX> in (a) the Olkiluoto mica gneiss and (b) Asan gneiss (Yim et al., 2022) samples with respect to changes in the orientation of the weak planes$ 그림 Fig. 8. Variations of apparent elastic shear modulus $\tilde{G}_{12}$ in (a) the Olkiluoto mica gneiss and (b) Asan gneiss (Yim et al., 2022) samples with respect to changes in the orientation of the weak planes
$Fig. 9. Variations of apparent elastic shear moduli (a) <TEX>$\tilde{G}_{12}$</TEX> and (b) <TEX>$\tilde{G}_{31}$</TEX> in the O Barco de Valdeorras slate sample with respect to changes in the orientation of the weak planes$ 그림 Fig. 9. Variations of apparent elastic shear moduli (a) $\tilde{G}_{12}$ and (b) $\tilde{G}_{31}$ in the O Barco de Valdeorras slate sample with respect to changes in the orientation of the weak planes
$Fig. 10. Variations of apparent Poisson's ratio (a) <TEX>$\tilde{\nu}_{12},\,(b)\,\tilde{\nu}_{23}\,and\,(c)\,\tilde{\nu}_{31} $</TEX> in the Asan gneiss (Cho et al., 2012) sample with respect to changes in the orientation of the weak planes$ 그림 Fig. 10. Variations of apparent Poisson's ratio (a) $\tilde{\nu}_{12},\,(b)\,\tilde{\nu}_{23}\,and\,(c)\,\tilde{\nu}_{31} $ in the Asan gneiss (Cho et al., 2012) sample with respect to changes in the orientation of the weak planes
$Fig. 11. Variations of apparent Poisson's ratio (a) <TEX>$\tilde{\nu}_{12},\,(b)\,\tilde{\nu}_{23}\,and\,(c)\,\tilde{\nu}_{31} $</TEX> in the O Barco de Valdeorras slate sample with respect to changes in the orientation of the weak planes$ 그림 Fig. 11. Variations of apparent Poisson's ratio (a) $\tilde{\nu}_{12},\,(b)\,\tilde{\nu}_{23}\,and\,(c)\,\tilde{\nu}_{31} $ in the O Barco de Valdeorras slate sample with respect to changes in the orientation of the weak planes

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