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Effects of Fracture Tensor Component and First Invariant on Block Hydraulic Characteristics of the 2-D Discrete Fracture Network Systems

절리텐서의 성분 및 일차불변량이 2-D DFN 시스템의 블록수리전도 특성에 미치는 영향

  • Um, Jeong-Gi (Department of Energy Resources Engineering, Pukyong National University)
  • 엄정기 (부경대학교 에너지자원공학과)
  • Received : 2019.01.07
  • Accepted : 2019.01.23
  • Published : 2019.02.28

Abstract

In this study, the effects of fracture tensor component and first invariant on block hydraulic behaviors are evaluated in the 2-D DFN(discrete fracture network) systems. A series of regression analysis is performed between connected fracture tensor components and block hydraulic conductivities estimated at every $30^{\circ}$ hydraulic gradient directions for a total of 36 DFN systems having various joint density and size distribution. The directional block hydraulic conductivity seems to have strong relation with the fracture tensor component estimated in direction perpendicular to it. It is found that an equivalent continuum approach could be acceptable for the 2-D DFN systems under condition that the first invariant of fracture tensor is more than 2.0~2.5. The first invariant of fracture tensor seems highly correlated with average block hydraulic conductivity and can be used to evaluate hydraulic characteristics of the 2-D DFN systems. Also, a possibility of upscaling using the first invariant of fracture tensor for the DFN system is addressed through this study.

Keywords

discontinuity;fracture tensor;discrete fracture network;fractured rock mass;block hydraulic conductivity

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Fig. 1. Solid angle, dΩ, in an upper hemisphere to estimate fracture tensor.

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Fig. 2. Comparison between directional block conductivity(k(p)) and connected fracture tensor component(CFTC) for different joint configurations of selected DFN systems; (a) & (b) D-1-1-*, (c) & (d) D2-2-*, (e) & (f) L1-3-*.

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Fig. 3. Relation between CFTC and directional conductivity factor(Kf) for DFN systems.

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Fig. 4. Effect of the first invariant(F0) of connectedfracture tensor on ER.

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Fig. 5. Relation between block conductivity factor and the first invariant of connected fracture tensor for DFN systems.

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Fig. 6. The connected flow network on a square window of size 20 m showing (a) before and (b) after correction using the first invariant of 2-D fracture tensor.

Table 1. Summary of input parameters for the generated DFN systems having different joint orientation, density and size.(after Han et al., 2017)

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Table 2. An example of fracture geometry before and after correction using the first invariant of 2-D fracture tensor

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Table 3. Estimated directional block conductivity in different direction and average block conductivity for the DFN systems having fracture geometry in Table 2

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Acknowledgement

Supported by : 부경대학교

References

  1. Fu, P. and Dafalias, Y.F. (2015) Relationship between void- and contact normal-based fabric tensors for 2D idealized granular materials. Int. J. Soilds Struct., v.63, p.68-81. https://doi.org/10.1016/j.ijsolstr.2015.02.041
  2. Han, J. and Um, J. (2016) Effect of joint orientation distribution on hydraulic behavior of the 2-D DFN system. Economic and Environmental Geology, v.49, p.31-41. https://doi.org/10.9719/EEG.2016.49.1.31
  3. Han, J., Um, J. and Lee, D. (2017) Effects of joint density and size distribution on hydrogeologic characteristics of the 2-D DFN system. Economic and Environmental Geology, v.50, p.61-71. https://doi.org/10.9719/EEG.2017.50.1.61
  4. Kanatani, K.I. (1984) Distribution of directional data and fabric tensors. Int. J. Eng. Sci., v.22, p.149-164. https://doi.org/10.1016/0020-7225(84)90090-9
  5. Kulatilake, P.H.S.W., Ucpirti, H. and Stephansson, O. (1994) Effect of finite size joints on the deformability of jointed rock at the two dimensional level. Can. Geotech. J., v.31, p.364-374. https://doi.org/10.1139/t94-044
  6. Li, X. and Li, X.S. (2009) Micro-macro quantification of the internal structure of granular materials. J. Eng. Mech., ASCE, v.135, p.641-656. https://doi.org/10.1061/(ASCE)0733-9399(2009)135:7(641)
  7. Mahtab, M.A. and Yegulalp, T.M. (1984) A similarity test for grouping orientation data in rock mechanics, Proc. of the 25th U.S. Symp. on Rock Mech., p.495-502.
  8. Miller, S.M. (1983) A statistical method to evaluate homogeneity of structural populations. Mathematical Geology, v.15, p.317-328. https://doi.org/10.1007/BF01036073
  9. Oda, M. (1982) Fabric tensor for discontinuous geological materials. Soils Found., v.22, P.96-108. https://doi.org/10.3208/sandf1972.22.4_96
  10. Panda, B.B. and Kulatilake, P.H.S.W. (1999) Relations between fracture tensor parameters and jointed rock hydraulics, J. Eng. Mech., v.125, p.51-59. https://doi.org/10.1061/(ASCE)0733-9399(1999)125:1(51)
  11. Rothenburg, L. and Bathurst, R.J. (1992) Micromechanical features of granular assemblies with planar elliptical particles. Geotechnique, v.42, p.79-95. https://doi.org/10.1680/geot.1992.42.1.79
  12. Satake, M. (1982) Fabric tensor in granular materials. in Vermeer, P.A. and Luger, H.J. (eds.), Proc. IUTAM Symp. on Deformation and Failure of Granular Materials. A.A. Balkema, Rotterdam, p.63-68.
  13. Wang, M., Kulatilake, P.H.S.W., Panda, B.B. and Rucker, M.L. (2001) Groundwater resources evaluation case study via discrete fracture flow modeling, Engineering Geology, v.62, p.267-291. https://doi.org/10.1016/S0013-7952(01)00029-1