[논문]삼차원 절리텐서 파라미터가 절리성 암반의 변형특성에 미치는 영향

류성진; 엄정기

doi:10.7474/tus.2021.31.1.066

삼차원 절리텐서 파라미터가 절리성 암반의 변형특성에 미치는 영향
Effects of 3-D Fracture Tensor Parameters on Deformability of Fractured Rock Masses 원문보기

터널과 지하공간: 한국암반공학회지 = Tunnel and underground space, v.31 no.1, 2021년, pp.66 - 81

류성진 (부경대학교 산학협력단) , 엄정기 (부경대학교 에너지자원공학과)

초록
AI-Helper

본 연구는 삼차원 절리텐서 파라미터와 DFN(discrete fracture network) 블록의 변형특성 간의 상관성 분석을 수행하여 절리텐서의 방향성분 및 일차불변량이 절리성 암반의 변형계수 및 전단탄성계수에 미치는 영향을 평가하였다. 확정적 방향성을 갖는 1~2개의 절리군을 사용하여 절리의 빈도 및 길이분포의 변화에 따라 생성한 총 224개의 DFN 블록에 대하여 절리텐서 파라미터가 산정되었다. 또한, 정육면체 DFN 블록에 대하여 개별요소법을 활용하여 서로 직교하는 세 방향으로 변형특성이 추정되었다. 절리텐서의 일차불변량이 증가할수록 변형계수 및 전단탄성계수는 대체로 저감되는 양상을 나타내지만, 감소폭이 줄어들어 일차불변량이 특정 기준값을 상회하면 변형계수 및 전단탄성계수는 거의 일정한 값을 유지하였다. 삼차원 DFN 블록에 대한 지향적 변형특성은 대응하는 방향의 절리텐서성분과 멱함수의 강한 상관관계를 도출하였다.

Abstract ▼ AI-Helper

The effects of directional fracture tensor components and first invariant of fracture tensor on deformation moduli and shear moduli of fractured rock masses is analyzed based on regression analysis performed between 3-D fracture tensor parameters and deformability of DFN blocks. Using one or two deterministic joint sets, a total of 224 3-D discrete fracture network (DFN) cube blocks were generated with various configurations of deterministic density and probabilistic size distribution. The fracture tensor parameters were calculated for each generated DFN systems. Also, deformability moduli with respect to three perpendicular direction of the DFN cube blocks were estimated based on distinct element method. The larger the first invariant of fracture tensor, the smaller the values for the deformability moduli of the DFN blocks. These deformability properties present an asymptotic pattern above the certain threshold. It is found that power-law function describes the relationship between the directional deformability moduli and the corresponding fracture tensor components estimated in same direction.

주제어

표/그림 (15)

그림 Fig. 1. Unit sphere to define the solid angle dΩ (after Oda, 1982)
$Fig. 2. A selected example of polyhedral block system; (a) 10 m× 10 m× 10 m discrete fracture network system having 000º / 60º joint orientation and (b) corresponding block system using real and fictitious joints$ 그림 Fig. 2. A selected example of polyhedral block system; (a) 10 m× 10 m× 10 m discrete fracture network system having 000º / 60º joint orientation and (b) corresponding block system using real and fictitious joints
표 Table 1. Summary of joint geometry parameters in the DFN blocks
그림 Fig. 3. Stress paths to estimate directional deformation modulus of the DFN blocks; (a) x direction, (b) y direction and (c) z direction
표 Table 2. Input parameters used to perform 3DEC stress-strain analysis (after Ryu et al., 2020)
그림 Fig. 4. Stress paths to estimate shear modulus of the DFN blocks; (a) x and y direction, (b) x and y direction and (c) y and z direction
그림 Fig. 5. Nine monitoring points on each face of the DFN cube (Ryu et al., 2020)
그림 Fig. 6. Calculated directional stress-strain plots of the 10 m DFN cube having 000º /60º joint orientation
그림 Fig. 7. Variation on horizontal deformation modulus (GPa) of the DFN blocks having 000º /60º joint orientation with different joint density and size distribution; (a) total number of joint = 15, mean joint size = 1.5 m, and standard deviation of joint size = 1.0 m, (b) total number of joint = 30, mean joint size = 1.5 m, and standard deviation of joint size = 1.0 m, (c) total number of joint = 15, mean joint size = 3.0 m, and standard deviation of joint size = 2.0 m and (d) total number of joint = 30, mean joint size = 3.0 m, and standard deviation of joint size = 2.0 m
$Table 3. Estimated deformability and fracture tensor parameters of the DFN blocks having 030º /60º joint orientation$ 표 Table 3. Estimated deformability and fracture tensor parameters of the DFN blocks having 030º /60º joint orientation
$Fig. 8. Relations between directional deformation moduli and first invariant of fracture tensor with respect to joint orientation; (a) Ex/Ei vs. L1(F) for 000º /30º joint orientation, (b) Ex/Ei vs. l1(F) for 030º/60º joint orientation, (c) Ey/Ei vs. l1(F) for 000º /30º joint orientation, (d) Ey/Ei vs. l1(F) for 030º /60º joint orientation, (e) Ez/Ei vs. l1(F) for 000º /30º joint orientation and (f) Ez/Ei vs l1(F) for 030º/ 60º joint orientation$ 그림 Fig. 8. Relations between directional deformation moduli and first invariant of fracture tensor with respect to joint orientation; (a) E_x/E_i vs. L₁^(F) for 000º /30º joint orientation, (b) E_x/E_i vs. l₁^(F) for 030º/60º joint orientation, (c) Ey/Ei vs. l₁^(F) for 000º /30º joint orientation, (d) Ey/Ei vs. l₁^(F) for 030º /60º joint orientation, (e) Ez/Ei vs. l₁^(F) for 000º /30º joint orientation and (f) Ez/Ei vs l₁^(F) for 030º/ 60º joint orientation
$Fig. 9. Relations between shear moduli and first invariant of fracture tensor with respect to joint orientation; (a) Gxy/Gi vs. l1(F) for 000º /30º joint oreientation, (b) Gxy/Gi vs. l1(F) for 030º /60º joint orientation, (c) Gyz/Gi vs. l1(F) for 000º /30º joint orientation, (d) Gyz/Gi vs. l1(F) for 030º /60º joint orientation, (e) Gxz/Gi vs. l1(F) for 000º /30º joint orientation and (f) Gxz/Gi vs. l1(F) for 030º /60º joint orientation$ 그림 Fig. 9. Relations between shear moduli and first invariant of fracture tensor with respect to joint orientation; (a) G_xy/G_i vs. l₁^(F) for 000º /30º joint oreientation, (b) G_xy/G_i vs. l₁^(F) for 030º /60º joint orientation, (c) G_yz/G_i vs. l₁^(F) for 000º /30º joint orientation, (d) G_yz/G_i vs. l₁^(F) for 030º /60º joint orientation, (e) G_xz/G_i vs. l₁^(F) for 000º /30º joint orientation and (f) G_xz/G_i vs. l₁^(F) for 030º /60º joint orientation
$Fig. 10. Relations between directional deformation moduli and fracture tensor components for different DFN blocks; (a) Ex/Ei vs. Fxx, (b) Ey/Ei vs. Fyy and (c) Ez/Ei vs. Fzz$ 그림 Fig. 10. Relations between directional deformation moduli and fracture tensor components for different DFN blocks; (a) E_x/E_i vs. F_xx, (b) E_y/E_i vs. F_yy and (c) E_z/E_i vs. F_zz
$Fig. 11. Relations between shear moduli and corresponding fracture tensor components for different DFN blocks; (a) Gxy/Gi vs. Fxx+Fyy, (b) Gyz/Gi vs. Fyy+Fzz and (c) Gxz/Gi vs. Fxx+Fzz$ 그림 Fig. 11. Relations between shear moduli and corresponding fracture tensor components for different DFN blocks; (a) G_xy/G_i vs. F_xx+F_yy, (b) G_yz/G_i vs. F_yy+F_zz and (c) G_xz/G_i vs. F_xx+F_zz
$Fig. 12. Relations between DFN block deformability in any direction and corresponding fracture tensor components; (a) Em/Ei vs. Fp and (b) Gm/Gi vs. Fk+Fl$ 그림 Fig. 12. Relations between DFN block deformability in any direction and corresponding fracture tensor components; (a) E_m/E_i vs. F_p and (b) G_m/G_i vs. F_k+F_l

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