在真實大地環境中，岩體含有許多不連續面，如：裂縫、節理、劈理、層面及斷層等等。岩體的變形與破壞與地質不連續面的存在相當有關。在含有裂縫的材料中，裂縫尖端的應力強度因子為控制裂縫開始開裂及傳播的主要參數，且與材料強度有關，應力強度因子之大小與裂縫傾角、裂縫長度及材料異向性程度有關。本研究主要是利用邊界元素法來探討異向性岩石的裂縫傳播行為，包含應力強度因子與裂縫傾角及材料異向性的關係、異向性岩石之混合模態破裂韌度之量測及裂縫初始開裂角度與裂縫傳播路徑之預測及模擬。

在本研究中，等向性與異向性材料之裂縫尖端應力強度因子，是利用邊界元素法來求取，在邊界元素法的公式中，位移積分方程式僅運用於外部邊界；曳引力積分方程式僅運用於裂縫單邊，此種方法可以消除傳統數值方法重複劃分網格的缺點。利用這兩種積分方程式，可解出在外圍邊界上的未知位移及曳引力，及裂縫面上未知的裂縫相對位移，利用裂縫相對位移即可求出裂縫尖端之應力強度因子。本研究並探討不同裂縫傾角及異向性程度對應力強度因子的影響，且與前人計算應力強度因子之解析解或數值解進行比較，結果發現均相當接近及吻合。

另外，本研究提出一套巴西試驗的方法，可藉由具有裂縫之巴西試驗圓盤試體承受徑向載重結合邊界元素法分析，來測定異向性大理岩之混合模態破裂韌度。本研究採用含有明顯黑白紋理之大理岩為試驗材料，並假設其為橫向等向性岩石，經由試驗與數值分析結果，可成功地求得其在模態I、II及混合模態載重下之破裂韌度，發現當層面傾角越大時，裂縫破壞的模式會趨於混合模態，最後並且提出一套適用於異向性大理岩之破壞包絡線。

在本研究中，將邊界元素法結合最大周圍應力破壞準則來預測異向性材料之裂縫初始開裂角度及模擬異向性材料之裂縫傳播路徑，並將數值分析結果與前人在初始開裂角度之結果及本研究之試驗所觀察之傳播路徑結果進行比較。研究結果發現，數值分析結果與試驗結果均相當接近及吻合。因此，代表本研究所提出之裂縫傳播模式可準確的分析等向性及異向性材料之裂縫傳播行為。

本研究亦利用裂縫傳播模式來模擬邊坡坡壞面，此分析模式和一般常用的邊坡穩定分析模式之不同處在於：不需要預先定義出可能的破壞模式或是破壞滑動面，此模式可直接根據邊坡張力裂縫之幾何形狀來預測出可能發生破壞的滑動面，且可探討裂縫在受到混合模態載重及材料異向性影響之可能破壞滑動面。

Rock masses in nature contain numerous discontinuities as cracks, joints, cleavages, beddings and even faults etc. Deformation and failure of a rock mass is largely dependent on the presence of geological discontinuities such as cracks and faults. In the cracked material, the stress intensity factors (SIFs) at crack tips, which govern the crack propagation and are associated with the strength of the materials, are strongly affected by crack inclination angle, orientation of anisotropy. This study presents the development of a unified numerical framework based on the boundary element method (BEM) for modeling crack propagation behavior in anisotropic rocks.

In this study, a new formulation of the BEM, based on the relative displacements at the crack tip, is used to determine the mixed mode SIFs of isotropic and anisotropic rocks. The new BEM formulation is such that the displacement integral equation is only collocated on the outside boundary and the traction integral equation is only collocated on one side of the crack surface. A decoupling technique can be used to determine the mixed mode SIFs of isotropic and anisotropic rocks based on the relative displacements at the crack tip. Numerical examples for the determination of the mixed mode SIFs for anisotropic rocks with different crack inclination angle, crack length, and degree of material anisotropy are presented.

A systematic procedure for determining fracture toughness of an anisotropic marble using the diametral compressive test (Brazilian test) with a central crack on the discs is presented. Additionally, a novel formulation to increase the accuracy in Stress Intensity Factor (SIF) calculations using Boundary Element Method (BEM) is applied to determine the stress intensity factors and the fracture toughness of anisotropic rocks under mixed-mode loading. The marble with clear white-black foliation from Hualien (in eastern Taiwan), was selected for the Brazilian tests. Diametral loading was conducted on the Cracked Straight Through Brazilian Disc (CSTBD) specimens to evaluate their fracture toughness. In addition, a new fracture criterion was developed to predict pure mode I, pure mode II or mixed mode I-II fracture toughness of the anisotropic marble. The new fracture criterion of anisotropic marble is based on the examination of mode I, mode II and mixed mode I-II fracture toughness for different crack angles and anisotropic orientation.

In this study, the BEM formulation combined with the maximum circumferential stress criterion was used to predict the crack initiation angles and to simulate the crack propagation paths. To demonstrate the proposed BEM procedure to predict crack propagation in anisotropic rocks, the propagation path in CSTBD specimen was numerically predicted and compared with the actual laboratory observations. Good agreement is found between the two approaches. It is therefore concluded that the proposed BEM procedure can accurately simulate the process of crack propagation for anisotropic rocks.

This study also presents a fracture propagation analysis for simulating the process of slope failure. Unlike the conventional slope stability analysis, the failure mode or the failure plane does not need to pre-defined. The development of the simulating failure surface is subjected to the fracture propagation under mixed mode constraints.

1. Aliabadi, M.H., 1997. Boundary element formulation in fracture mechanics. Applied Mechanics Review, ASME 50, 83-96.
2. Aliabadi, M.H., 1997. A new generation of boundary element methods in fracture mechanics. International Journal of Fracture 86, 91-125.
3. Al-Shayea, N.A., 2005. Crack propagation trajectories for rocks under mixed mode I-II fracture. Engineering Geology 81, 84-97.
4. Amadei, B., 1983. Rock Anisotropy and the Theory of Stress Measurements, Springer-Verlag, New York.
5. Amadei, B., Pan, E., 1992. Gravitational stresses in anisotropic rock masses with inclined strata. International Journal of Rock Mechanics and Mining Sciences 29, 225-236.
6. Ammons, B.A., Vable, M., 1996. Boundary element analysis of cracks. International Journal of Solids and Structures 33, 1853-1865.
7. Atkinson, C., Smelser, R.E., Sanchez, J., 1982. Combined mode fracture via the cracked Brazilian disk test. International Journal of Fracture 18, 279-291.
8. Awaji, H., Sato, S., 1978. Combined mode fracture toughness measurement by the disk test. Journal of Engineering Materials and Technology, Transaction of the ASME 100(4), 175-182.
9. Ayatollahi, M.R., Aliha, M.R.M., 2006. On determination of mode II fracture toughness using semi-circular bend specimen. International Journal Solids and Structures 43, 5217-5227.
10. Backers, T., Fardin, N., Dresen, G., Stephansson, O., 2003. Effect of loading rate on Mode I fracture toughness, roughness and micromechanics of sandstone. International Journal of Rock Mechanics and Mining Sciences 40, 425-433.
11. Bearman, R.A., 1999. The use if the point load test for the rapid estimation of Mode I fracture toughness. International Journal of Rock Mechanics and Mining Sciences 36, 257-263.
12. Becker, A.A., 1992. The Boundary Element Method in Engineering. McGraw-Hill Book Company, UK.
13. Blandford, G.E., Ingraffea, A.R., Liggett, J.A., 1981. Two-dimensional stress intensity factor computations using the boundary element method. International Journal for Numerical Methods in Engineering 17, 387-404.
14. Bobet, A., 2000. Modelling of crack initiation, propagation and coalescence in uniaxial compression. Rock Mechanics and Rock Engineering 33(2), 119-139.
15. Bouchard, P.O., Bay, F., Chastel, Y., Tovena, I., 2000. Crack propagation modeling using an advanced remeshing technique. Computer Methods in Applied Mechanics and Engineering 189, 723-742.
16. Broek, D., 1988. The Practical Use of Fracture Mechanics, Kluwer Academic Publishers, London.
17. Cerrolaza, M., Alarcon, E., 1989. A bi-cubic transformation for the numerical evaluation of the Cauchy principal value integrals in boundary methods. International Journal for Numerical Methods in Engineering 28, 987-999.
18. Chen, C.S, Pan, E., Amadei, B., 1998. Determination of Deformability and Tensile Strength of Anisotropic Rock Using Brazilian Tests. International Journal of Rock Mechanics and Mining Sciences 35(1), 43-61.
19. Chen, C.S., 1996. Characterization of deformability, strength, and fracturing of anisotropic rocks using Brazilian tests, Ph.D. thesis, Department of Civil Engineering, University of Colorado.
20. Chen, C.S., Pan, E., Amadei, B., 1998. Fracture mechanics analysis of cracked discs of anisotropic rock using the boundary element method. International Journal of Rock Mechanics and Mining Sciences 35(2), 195-218.
21. Chen, J.T., Hong, H.K., 1999. Review of dual boundary element methods with emphasis on hypersingular integrals and divergent series. Applied Mechanics Review, ASME 52(1), 17-33.
22. Chen, Y.Z., 1995. Hypersingular integral equation approach for the multiple crack problem in an infinite plate. Acta Mechanica 108, 121-131.
23. Chong, K.P., Kuruppu, M.D., Kuszmaul, J.S., 1987. Fracture toughness determination of rocks with core-based specimens. SEM/RILEM International Conference on Fracture of Concrete and Rocks, Texas, 13-25.
24. Cisilino, A.P., Aliabadi, M.H., 1999. Three-dimensional boundary element analysis of fatigue crack growth in linear and non-linear fracture problems. Engineering Fracture Mechanics 63, 713-733.
25. Coggan, J.S., Stead, D., Howe, J.H., 2000. Characterisation of a structurally controlled flowslide in a kaolinised granite slope. In: Bromhead, E., Dixon, N., Ibsen, M.-L. (Eds.), Proceedings of 8th International Symposium on Landslides, Landslides in Research, Theory and Practice. Cardiff 1, 299-304.
26. Crouch, S.L., Starfield, A.M., 1983. Boundary Element Methods in Solid Mechanics, George Allen and Unwin Publishers, London.
27. Cruse, T.A., 1972. Surface Cracks: Physical Problems and Computational Solutions. J.L. Swedlow (ed.), American Society of Mechanical Engineers, New York, 153-170.
28. Dong, S., Wang, Y., Xia, Y., 2004. Stress intensity factors for central cracked circular disk subjected to compression. Engineering Fracture Mechanics 71, 1155-1168.
29. Dwyer, J.F., Pan, E., 1995. Edge function analysis of stress intensity factors in cracked anisotropic plates. International Journal of Fracture 72 327-342.
30. Erdogan, F., Sih, G.C., 1963. On the crack extension in plates under loading and transverse shear. Journal of Basic Engineering 85, 519-527.
31. Fischer, M.P., Elsworth, D., Alley, R. B., Engelder, T., 1996. Finite element analysis of the modified ring test for determining mode I fracture toughness. International Journal of Rock Mechanics and Mining Sciences 33(1), 1-15.
32. Fowell, R.J., Xu, C., 1994. The use of the cracked Brazilian disc geometry for rock fracture investigations. International Journal of Rock Mechanics and Mining Sciences 31(6), 571-579.
33. Fowell, R.J., 1995. Suggested method for determining mode I fracture toughness using cracked chevron notched Brazilian disk (CCNBD) specimen. International Journal of Rock Mechanics and Mining Sciences 32, 57-64.
34. Gandhi, K.R., 1972. Analysis of inclined crack centrally placed in an orthotropic rectangular plate. Journal of Strain Analysis 7(3), 157-162.
35. Gary, L.J., Martha, L.F., Ingraffea, A.R., 1990. Hypersingular integrals in boundary element fracture analysis. International Journal for Numerical Methods in Engineering 29, 1135-1158.
36. Germanovich, L.N., Salganik, R.L., Dyskin, A.V., Lee, K.K., 1994. Mechanisms of brittle fracture of rocks with multiple pre-existing cracks in compression. Pure and Applied Geophysics 143(1/2/3) 117-149.
37. Germanovich, L.N., Ring, L.M., Carter, B.J., Ingraffea, A.R., Dyskin, A.V., Ustinov, K.B., 1995. Simulation of crack growth and interaction in compression, Proceedings of the 8th International Conference on Rock Mechanics 1, Rotterdam and Brookfield: Balkema, 219-226.
38. Germanovich, L.N., Carter, B.J., Ingraffea, A.R., Dyskin, A.V., Lee, K.K., 1996. Mechanics of 3-D crack growth under compressive loads. In: Aubertin, M., Hassani, F., Mitri, H., (eds.), Rock mechanics tools and techniques. Proceedings of the 2nd North American Rock Mechanics Symposium: NARMS’96. Rotterdam and Brookfield: Balkema, 1151-1160.
39. Germanovich, L.N., Dyskin, A.V., 2000. Fracture mechanisms and instability of openings in compression. International Journal of Rock Mechanics and Mining Sciences 37, 263-284.
40. Griffith, A.A., 1921. The phenomena of rupture and flow in solids. Philosophical Transaction Royal Society A221, 163.
41. Griffith, A.A., 1924. The theory of rupture, Proceedings of the 1st International Congress of Applied Mechanics, Delft, 55-63.
42. Gunsallus, K.L., Kulhawy, F.H., 1984. A comparative evaluation of rock strength measures. International Journal of Rock Mechanics and Mining Sciences 21(5), 233-248.
43. Guo, H., Aziz, N.I., Schmidt, L.C., 1993. Rock fracture toughness determination by the Brazilian test. Engineering Geology 33, 177-188.
44. Hallbauer, D.K., Wagner, H., Cook, N.G.W., 1973. Some observations concerning the microscopic and mechanical behavior of quartzite specimens in stiff triaxial compression tests. International Journal of Rock Mechanics and Mining Sciences 10, 713-726.
45. Hoek, E., Bieniawski, Z.T., 1965. Brittle fracture propagation in rock under compression. International Journal of Fracture 1, 137-155.
46. Hong, H.K., Chen, J.T., 1988. Derivations of integral equations of elasticity. Journal of Engineering Mechanics 114, 1028-1044.
47. Hsiao, Y.C., 2000. The Study of Mechanical Anisotropy on Marble. M.S. Thesis, National Taipei University of Technology, 130 pp. (in Chinese)
48. Hsu, S.C., 2000. Determination of Tensile Strength of Anisotropic Rocks. M.S. Thesis, National Cheng Kung University, 108 pp. (in Chinese)
49. Ingraffea, A.R., Gunsallus, K.L., Beech, J.F., Nelson, P.P., 1984. A short-rod based system for fracture toughness testing of rock. Chevron-Notched Specimens: Testing and Stress Analysis, ASTM STP 855, American Society for Testing and Materials, 152-166.
50. Irwin, G.R., 1957. Analysis of stresses and strains near the end of a crack. Journal of Applied Mechanics 24, 361-364.
51. Isida, M., 1975. Arbitrary loading problems of doubly symmetric regions containing a central crack. Engineering Fracture Mechanics 7, 505-514.
52. Itasca, 2004. Itasca Software Products—FLAC, FLAC3D, UDEC, 3DEC, PFC, PFC3D. Itasca Consulting Group Inc., Minneapolis.
53. Jing, L., 2003. A review of techniques, advances and outstanding issues in numerical modelling for rock mechanics and rock engineering. International Journal of Rock Mechanics and Mining Sciences 40, 283-353.
54. Kalkani, E.C., Piteau, D.R., 1976. Finite element analysis of toppling failure at Hell’s Gate Bluffs. British Columbia. Bulletin of International Association of Engineering Geology XIII (4), 315-327.
55. Krahn, J., Morgenstern, N.R., 1976. The mechanics of the Frank Slide. Rock Engineering for Foundations and Slopes. Proceedings of ASCE Geotechnical Engineering Specialty Conference, Boulder. ASCE, New York, 309-332.
56. Krishnan, G.R., Zhao, X.L., Zaman, M., Roegiers, J.C., 1998. Fracture toughness of a soft sandstone. International Journal of Rock Mechanics and Mining Sciences 35(6), 695-710.
57. Ku, C.Y., 2001. Modeling of jointed rock masses based on the numerical manifold method. Ph.D. Dissertation, Department of Civil and Environmental Engineering, University of Pittsburgh.
58. Lekhnitskii, S.G., 1981. Theory of elasticity of an anisotropic elastic body, translated by Fern, P., Holden-Day Inc., San Francisco.
59. Leung, A.Y.T., Su, R.K.L., 1995. Body-force linear elastic stress intensity factor calculation using fractal two level finite element method. Engineering Fracture Mechanics 51(6), 879-888.
60. Libatskii, L.L., Kovchik, S.E., 1967. Fracture of discs containing cracks. Soviet Materials Science 3, 334-339.
61. Lim, I.L., Johnston, I.W., 1993. Stress intensity factors for semi-circular specimens under three-point bending. Engineering Fracture Mechanics 44(3), 363-382.
62. Lim, I.L., Johnston, I.W., Choi, S.K., Boland, J.N., 1994. Fracture testing of a soft rock with semi-circular specimens under three-point bending. Part 2: Mixed-mode. International Journal of Rock Mechanics and Mining Sciences 31(3), 185-197.
63. Murakami, Y., 1976. A simple procedure for the accurate determination of stress intensity factors by finite element method. Engineering Fracture Mechanics 8, 643-655.
64. Murakami, Y., 1987. Stress Intensity Factors Handbook, Pergamin Press, Oxford.
65. Ouchterlony, F., 1987. A presentation of the ISRM suggested methods for determining fracture toughness of rock materials. Proceedings of the 6th International Conference on Rock Mechanics 2, Balkema, Rotterdam, 1181-1186.
66. Ouchterlony, F., 1988. Suggested methods for determining the fracture toughness of rock. International Journal of Rock Mechanics and Mining Sciences 25(2), 71-69.
67. Palaniswamy, K., Knauss, W.G., 1972. Propagation of a crack under general, in-plane tension. International Journal of Fracture 8(B7), 114-117.
68. Pan, E., Amadei, B., 1996. Fracture mechanics analysis of cracked 2-D anisotropic media with a new formulation of the boundary element method. International Journal of Fracture 77, 161-174.
69. Pan, E., 1997. A general boundary element analysis of 2-D linear elastic fracture mechanics. International Journal of Fracture 88, 41-59.
70. Pan, E., Chen, C.S., Amadei, B., 1997. A BEM formulation for anisotropic half-plane problems. Engineering Analysis with Boundary Elements 20, 185-195.
71. Peng, S., Johnson, A.M., 1972. Crack growth and faulting in cylindrical specimens of Chelmsford granite. International Journal of Rock Mechanics and Mining Sciences 9, 37-86.
72. Portela, A., 1992. Dual Boundary Element incremental Analysis of Crack Growth, Ph.D. Thesis, Wessex Institute of Technology, Portsmouth University, Southampton, UK.
73. Portela, A., Aliabadi, M.H., Rooke, D.P., 1992. The dual boundary element method: Effective implementation for crack problems. International Journal for Numerical Methods in Engineering 33, 1269-1287.
74. Portela, A., 1993. Dual Boundary Element Analysis of Crack Growth, Computational Mechanics Publications, Southampton UK and Boston USA.
75. Portela, A., Aliabadi, M.H., Rooke, D.P., 1993. Dual Boundary Element incremental Analysis of Crack Growth. Composite Structures 46(2), 237-284.
76. Rooke, D.P., Tweed, J., 1973. The stress intensity factors of a radial crack in a point loaded disc. International Journal of Engineering Science 11, 285-290.
77. Richard, H.A., 1984. Examination of brittle fracture criteria for overlapping mode I and mode II loading applied to cracks. In Application of Fracture Mechanics to Materials and Structures, G.C. Sih et al. (eds.), Martinus Nijhoff Publication, 309-316.
78. Sato, A., Hirakawa, Y., Sugawara, K., 2001. Mixed mode crack propagation of homogenized cracks by the two-dimensional DDM analysis. Construction and Building Materials 15, 247-261.
79. Scavia, C., 1995. A method for the study of crack propagation in rock structures. Geotechnique 45(3), 447-463.
80. Shen, B., Stephansson, O., 1994. Modification the G-criterion for crack propagation subjected to compression. Engineering Fracture Mechanics 47(2), 177-189.
81. Shetty, D.K., Rosenfield, A.R., Duckworth, W.H., 1985. Fracture toughness of ceramics measured by a chevron-notched diametral compression test. Journal of the American Ceramic Society 68(12), c325-c443.
82. Shetty, D.K., Rosenfield, A.R., Duckworth, W.H., 1986. Mixed-mode fracture of ceramic in diametral compression. Journal of the American Ceramic Society 69(6), 437-443.
83. Shetty, D.K., Rosenfield, A.R., Duckworth, W.H., 1987. Mixed mode fracture in biaxial stress state: Application of the diametrical-compression (Brazilian disk) test. Engineering Fracture Mechanics 26(3), 825-845.
84. Sih, G.C., Paris, P.C., Irwin, G.R., 1965. On cracks in rectilinearly anisotropic bodies. International Journal of Fracture, 3, 189-203.
85. Sih, G.C., 1974. Strain energy density factor applied to mixed mode crack problems. International Journal of Fracture 10(B7), 305-321.
86. Sollero, P., Aliabadi, M.H., 1993. Fracture mechanics analysis of anisotropic plates by the boundary element method. International Journal of Fracture 64, 269-284.
87. Sollero, P., Aliabadi, M.H., Rooke, D.P., 1994. Anisotropic analysis of cracks emanating from circular holes in composite laminates using the boundary element method. Engineering Fracture Mechanics 49, 213-224.
88. Sollero, P., Aliabadi, M.H., 1995a. Anisotropic analysis of cracks in composite laminates using the dual boundary element method. Composite Structures 31, 229-233.
89. Sollero, P., Aliabadi, M.H., 1995b. Dual boundary element analysis of anisotropic crack problems. In boundary Elements XVII, C.A. Brebbia et al. (eds.), Computational Mechanics Publications, Southampton, 267-278.
90. Snyder, M.D., Cruse, T.A., 1975. Boundary-integral equation analysis of cracked anisotropic plates. International Journal of Fracture 11, 315-328.
91. Stacey, T.R., Xianbin, Y., Armstrong, R., Keyter, G.J., 2003. New slope stability considerations for deep open pit mines. Journal of the South African Institute of Mining and Metallurgy 103, 373-389.
92. Stead, D., Eberhardt, E., Coggan, J.S., 2006. Developments in the characterization of complex rock slope deformation and failure using numerical modelling techniques. Engineering Geology 83, 217-235.
93. Steif, P.S., 1984. Crack extension under compressive loading. Engineering Fracture Mechanics 20(3), 463-473.
94. Sun, Z., Ouchterlony, F., 1986. Fracture toughness of Stripa granite cores. International Journal of Rock Mechanics and Mining Sciences 23(6), 399-409.
95. Suo, Z., 1990. Singularities, interfaces and cracks in dissimilar anisotropic media. Proceedings of the Royal Society of London, Series A, Mathematical and Physical Sciences 427, 331-358.
96. Swan, G., Alm, O., 1982. Sub-critical crack growth in Stripa granite: Direct observations. Proceedings of the 23rd U.S. Symposium on Rock Mechanics, University of California, Berkeley, 542-550.
97. Tada, H., Paris, P.C., Irwin. G.R., 1985. The Stress Analysis of Cracks Handbook, 2nd edition, Paris Productions Incorporated, Missouri.
98. Tahan, W.W., Staab, G.H., Advani, S.H., Lee, J.K., 1990. A mixed-mode local symmetric fracture criterion for geo-materials. Proceedings of the 31st U.S. Symposium on Rock Mechanics, 455-462.
99. Turner, F.J., Weiss, L.E., 1963. Structural Analysis of Metamorphic Tectonites. McGraw-Hill, New York.
100. Vallejo, L.E., 1987. The brittle and ductile behavior of a material containing a crack under mixed-mode loading. Proceedings of the 28th U.S. Symposium on Rock Mechanics, University of Arizona, Tucson.
101. Wang, Q.Z., Jia, X.M., Kou, S.Q., Zhang, Z.X., Lindqvist, P.-A., 2003. More accurate stress intensity factor derived by finite element analysis for the ISRM suggested rock fracture toughness specimen－CCNBD. International Journal of Rock Mechanics and Mining Sciences 40, 233-241.
102. Wong, R.H.C., Chau, K.T., Tang, C.A., Lin, P., 2001. Analysis of crack coalescence in rock-like materials containing three flaws-Part I: experimental approach. International Journal of Rock Mechanics and Mining Sciences 38, 909-924.
103. Whittaker, B.N., Singh, R.N., Sun, G., 1992. Rock Fracture Mechanics Principles, Design and Applications, Developments in Geotechnical Engineering. Elsevier Publishers, Netherlands.
104. Woo, C.W., Ling, L.H., 1984. On angled crack initiation under biaxial loading. Journal of Strain Analysis 19(1), 51-59.
105. Wu, X., Li, X., 1989. Analysis and modification of fracture criteria for mixed-mode crack. Engineering Fracture Mechanics 34(1), 55-64.
106. Wyllie, D.C., Mah, C.W., 2004. Rock Slope Engineering. Spon Press, USA and Canada.
107. Zhao, X.L., Roegiers, J.-C., Chen, J., 1994. Mixed-mode fracture propagation in fractured rock. In Computer Methods and Advances in Geomechanics, Siriwardane and Zaman (eds.), Bailema, Rotterdam.