本文以顆粒流軟體PFC3D（Particle Flow Code3D）模擬不同裂隙幾何條件的裂隙岩體，以探討其力學行為。透過FracMan軟體於指定尺寸之岩體模型內部生成離散裂隙網絡（discrete fracture network, DFN），再以顆粒流軟體PFC3D將裂隙資料套入平滑節理模型（smooth joint model, SJM）結合鍵結顆粒模型（bonded particle model, BPM）以生成合成岩體（synthetic rock mass, SRM），模擬巨觀橫向等向性與巨觀等向性裂隙岩體在三軸壓縮試驗下的力學行為，計算其最大主應力（σ1）、楊氏模數（E50）、裂縫數目、應力與軸向應變及體積應變（volumetric strain）與軸向應變關係。
本文之研究項目為：（1）設定一系列之參數以研究裂隙程度與裂隙尺寸對於裂隙岩體在力學行為上的影響。（2）選用現地裂隙資料為均勻隨機分佈（κ = 0）的裂隙組，用以生成等向性岩體以進行三軸壓縮試驗，藉此觀察其破壞過程與破壞模態，並與Basu et al.（2013）的單軸試驗觀察、Bieniawski（1967）、Wawersik and Fairhust （1970）和Elliott（1982）的三軸試驗結果進行比較。（3）設定七種角度之單一裂隙組，用於生成橫向等向性岩體以進行三軸（含單軸）試驗，藉此觀察其破壞過程與破壞模態，其中，以Tien et al.（2006）和Khanlari et al.（2014）的試驗觀察與本試驗之破壞模態相比，並與Tien and Kuo（2001）的破壞準則進行比較。（4）生成一至四組裂隙組數的合成岩體進行單壓試驗，以驗證Hoek and Brown（1980, 1988）提出的概念性模式，同時以Amadei（1983）提出之橫向等向性岩體之彈性常數決定方法，驗證單一組裂隙組之橫向等向性岩體的楊氏模數之準確性。

This paper presents the mechanical behaviors of fractured rock masses for various geometrical conditions by using the Particle Flow Code (PFC3D). A specified rock mass size is assigned by software FracMan to generate discrete fracture network (DFN) then the fracture data were input into smooth joint model (SJM), combing with bonded particle model (BPM) by PFC3D to produce synthetic rock mass (SRM). SRM was used to simulate the mechanical behaviors based on macroscopically isotropic/anisotropic rock under triaxial test, calculating major principal stress, young's modulus, crack numbers, stress-axial strain relationship and volumetric strain-axial strain relationship.
The research projects are including: (1) Set a series of parameters to study the effect of the fracture intensity and the fracture size on the mechanical behaviors of the fractured rock mass. (2) Select one set of in-situ fracture data which was uniformly random distribution (κ = 0) to generate isotropic rock for triaxial test then observe the failure process and the failure mode. Compare our result with the uniaxial test observations of Basu et al. (2013), and the triaxial test result of Bieniawski (1967), Wawersik and Fairhust (1970) and Elliott (1982). (3) Set up single fracture set of seven angles to generate anisotropic rock for triaxial test then observe the failure process and the failure mode. The experimental results of Tien et al. (2006) and Khanlari et al. (2014) were compared with the failure mode of the test, and the maximum principal stress of the test results was compared with the failure criteria proposed by Tien and Kuo (2006). (4) To verify the conceptual model proposed by Hoek and Brown (1980, 1988), generating SRM with one to four sets of fracture then act the uniaxial test. Furthermore, to verify the accuracy of the Young’s modulus of the transversely isotropic rock mass of one set of fracture, using the method proposed by Amadei (1983) to determine elastic constants of the transversely isotropic rock mass.

1. 郭明傳，「複合岩體之岩塊體積比量測及其力學行為」，博士論文 (2005)。
2. 劉文智，「以數值模擬層狀岩石巴西試驗」，碩士論文 (2013)。
3. 法麗佳，「針對裂隙岩體裂隙程度(P32)與水利傳導係數之表徵單元體積(REV)進行探討」，碩士論文 (2017)。
4. 許哲睿，「岩體裂隙程度與力學性質之不確定性」，碩士論文 (2017)。
5. Amadei, B., Influence of Rock Anisotropy on Stress Measurements by Overcoring Techniques, Rock Anisotropy and the Theory of Stress Measurements, Springer, Berlin, Heidelberg, pp. 189-241 (1983).
6. Arzúa, J., Alejano, L.R., and Walton, G., “Strength and dilation of jointed granite specimens in servo-controlled triaxial tests,” Int J Rock Mech Min Sci, Vol. 69, pp. 93-104 (2014).
7. Bieniawski, Z.T., “Mechanism of brittle fracture of rock: Part II—experimental studies,” Int J Rock Mech Min Sci, Vol. 4, pp. 407-423 (1967).
8. Brady, B.H.G., and Brown, E.T., FRACMESH -A Program for the Generation of Finite-Element Meshes for the Hydrodynamic Modelling of Fractured Rocks, Nagra (1994).
9. Brady, B.H.G., and Brown, E.T., Rock Mechanics for underground mining, Kluwer Academic Publishers, United States of America, pp. 133-136 (2004).
10. Cundall, P.A., Pierce, M.E., and Ivars, D.M., “Quantifying the Size Effect of Rock Mass Strength,” In: Proceedings of the 1st Southern Hemisphere International Rock Mechanics Symposium, Australian Centre for Geomechanics (ACG), Vol. 2, pp. 3-15, (2008).
11. Dershowitz, W.S., and Schrauf T.S., Discrete Fracture Flow Modeling With The Jinx Package, American Rock Mechanics Association, American (1987).
12. Duan, K., and Kwok, C.Y., “Discrete element modeling of anisotropic rock under Brazilian test conditions,” Int J Rock Mech Min Sci, Vol. 78, pp. 45-56 (2015).
13. Elmo, D., Rogers, S., Stead, D., and Eberhardt, E., “Discrete Fracture Network approach to characterise rock mass fragmentation and implications for geomechanical upscaling,” Mining Technology, Vol.123(3), pp. 149-161 (2014).
14. Elliott, G.M., “An Investigation of a Yield Criterion for Rock,” Ph.D. Dissertation, University of London, United Kingdom (1982).
15. Esmaieli, K., Hadjigeorgiou, J., and Grenon, M., “Estimating geometrical and mechanical REV based on synthetic rock mass models at Brunswick Mine,” Int J Rock Mech Min Sci, Vol. 47, pp. 915-926 (2010).
16. Hawkes, I., and Mellor. M., “Uniaxial testing in rock mechanics laboratories,” Eng Geol, Vol. 4 pp. 179-285 (1970).
17. Hoek, E., and Brown, E.T., Underground Excavations in Rock, Taylor & Francis Group, United States of America (1980).
18. Hoek, E., and Brown, E.T., “The Hoek–Brown failure criterion—a 1988 update,” In: Curran J (ed) Proceedings of the 15th Canadian Rock Mechanics Symposium, University of Toronto, pp 31-38 (1988).
19. H"U" ̈rlimann, W., Splitting risk and premium calculation, Bulletin of the Swiss Association of Actuaries, pp. 229-249 (1994).
20. Herbert, A.W., “Modelling approaches for discrete fracture network flow analysis,” Dev Geotech Eng, Vol. 79, pp. 213-229 (1996).
21. Hutchinson, D.J., and Diederichs M.S., Cablebolting in underground mines, BiTech Publishers, Canada (1996).
22. Huang, D., Wang, J., and Liu, Su., “A comprehensive study on the smooth joint model in DEM simulation of jointed rock masses,” Granular Matter, Vol. 17(6), pp. 775-791 (2015).
23. Ivars, D.M., Pierce, M.E., and Darcel, C., “Anisotropy and scale dependency in jointed rock-mass strength – A Synthetic Rock Mass Study,” In: Proceedings of the 1st International FLAC/DEM Aymposium on Numerical Modeling, pp. 231-239 (2008).
24. Ivars, D.M., Pierce, M.E., Darcel, C., Reyes-Montes, J., Potyondy, D.O., Young, R.P., and Cundall, P.A., “The synthetic rock mass approach for jointed rock mass modelling,” Int J Rock Mech Min Sci, Vol. 48(2), pp. 219-244 (2011).
25. Itasca Consulting Group Inc. PFC3D(particle flow code in 3 dimensions), Version 5.0, MN 55401 (2013).
26. Jaeger, J.C., “Shear failure of anistropic rocks,” Geol Mag, Vol. 97(1) pp. 65-72 (1960).
27. Khanlari, G., Rafiei B., and Abdilor Y., “Evaluation of strength anisotropy and failure modes of laminated sandstones,” Arab J Geosci, Vol. 8, pp. 3089-3102 (2014).
28. Lim, S.S., Martin C.D., and Åkessonb, U., “In-situ stress and microcracking in granite cores with depth,” Eng Geol, Vol. 147-148(12), pp. 1-13 (2012).
29. Martin, C.D., “Seventeenth Canadian Geotechnical Colloquium: The effect of cohesion loss and stress path on brittle rock strength,” Can Geotech J, Vol. 34(5), pp. 698-725 (1997).
30. Min, K.B., and Jing, L., “Stress dependent mechanical properties and bounds of poisson's ratio for fractured rock masses investigated by a DFN-DEM technique,” Int J Rock Mech Min Sci, Vol. 41, pp. 390-395 (2004).
31. Potyondy, D.O., and Cundall, P.A., “A bonded-particle model for rock,” Int J Rock Mech Min Sci, Vol. 41(8), pp. 1329-1364 (2004).
32. Potyondy, D.O., “Simulating spalling, phase II: feasibility assessment,” Itasca Consulting Group Report to Svensk Karnbranslehantering AB (SKB), Stock- holm, Sweden, ICG09-2502-3F; January (2009).
33. Pierce, M., Ivars, D.M., and Sainsbury, B., “Use of Synthetic Rock Masses (SRM) to Investigate Jointed Rock Mass Strength and Deformation Behavior,” In: Anonymous proceedings of the international conference on rock joints and jointed rock masses, Tucson, Arizona, USA. (2009).
34. Schopfer, M.P.J., Abe, S., Childs, C., and Walsh, J.J., “The impact of porosity and crack density on the elasticity, strength and friction of cohesive granular materials: insights from DEM modeling,” Int J Rock Mech Min Sci, Vol. 46, pp. 250-261 (2009).
35. Scholtès, L., and Donze, F.V., “Modelling progressive failure in fractured rock masses using a 3D discrete element method,” Int J Rock Mech Min Sci, Vol. 52, pp. 18-30 (2012).
36. Tien, Y.M., and Kuo, M.C., “A failure criterion for transversely isotropic rocks,” Int J Rock Mech Min Sci, Vol. 38(3), pp. 399-412 (2001).
37. Tien, Y.M., Kuo, M. C., and Lu, Y.C., “Chapter 16: Failure criteria for transversely isotropic rock,” Rock Mechanics and Engineering, Volume 1: Principles, Ed. Feng, X.T., CRC Press, London, pp. 451-477 (2016).
38. Vazaios, I., Farahmand, K., Vlachopoulos, N., and Diederichs, M.S., “Effects of confinement on rock mass modulus: A synthetic rock mass modelling (SRM) study,” J Rock Mech Geotech, Vol. 10, pp. 436-456 (2018).
39. Wawersik, W.R., and Fairhurst, C., “A study of brittle rock fracture in laboratory compression experiments,” Int J Rock Mech Min Sci, Vol. 7, pp. 561-575 (1970).
40. Wang, T., Xu, D., and Elsworth, D., “Distinct element modeling of strength variation in jointed rock masses under uniaxial compression,” Geomech Geophys Geo-, Vol. 2, pp. 11-24 (2016).