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A review paper about experimental investigations on failure behaviour of non-persistent joint

  • Shemirani, Alireza Bagher (Department of Civil Engineering, Sadra Institute of Higher Education) ;
  • Haeri, Hadi (Young Researchers and Elite Club, Bafgh Branch, Islamic Azad University) ;
  • Sarfarazi, Vahab (Department of Mining Engineering, Hamedan University of Technology) ;
  • Hedayat, Ahmadreza (Department of Civil and Environmental Engineering, Colorado School of Mines)
  • Received : 2016.09.18
  • Accepted : 2017.03.21
  • Published : 2017.10.25
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Abstract

There are only few cases where cause and location of failure of a rock structure are limited to a single discontinuity. Usually several discontinuities of limited size interact and eventually form a combined shear plane where failure takes place. So, besides the discontinuities, the regions between adjacent discontinuities, which consist of strong rock and are called material or rock bridges, are of utmost importance for the shear strength of the compound failure plane. Shear behaviour of persistent and non-persistent joint are different from each other. Shear strength of rock mass containing non-persistent joints is highly affected by mechanical behavior and geometrical configuration of non-persistent joints located in a rock mass. Therefore investigation is essential to study the fundamental failures occurring in a rock bridge, for assessing anticipated and actual performances of the structures built on or in rock masses. The purpose of this review paper is to present techniques, progresses and the likely future development directions in experimental testing of non-persistent joint failure behaviour. Experimental results showed that the presence of rock bridges in not fully persistent natural discontinuity sets is a significant factor affecting the stability of rock structures. Compared with intact rocks, jointed rock masses are usually weaker, more deformable and highly anisotropic, depending upon the mechanical properties of each joint and the explicit joint positions. The joint spacing, joint persistency, number of rock joint, angle of rock joint, length of rock bridge, angle of rock bridge, normal load, scale effect and material mixture have important effect on the failure mechanism of a rock bridge.

Keywords

References

  1. Ashby, M.F. and Hallam, S.D. (1986), "The failure of brittle solids containing small cracks under compressive stress states", Acta Metall., 34(3), 497-510. https://doi.org/10.1016/0001-6160(86)90086-6
  2. Batzle, M.L., Simmons, G. and Siegfried, R.W. (1980), "Microcrack closure in rocks under stress: Direct observation", J. Geophys. Res., 85(B12), 7072-7090. https://doi.org/10.1029/JB085iB12p07072
  3. Bieniawski, Z.T. (1967), "Mechanism of brittle fracture of rock Part II-experimental studies", J. Rock Mech. Min. Sci. Geomech. Abstr., 4(4), 407-423. https://doi.org/10.1016/0148-9062(67)90031-9
  4. Bobet, A. (1997), "Fracture coalescence in rock materials: Experimental observations and numerical predictions", Sc.D. Dissertation, MIT, Cambridge, U.S.A.
  5. Bobet, A. (2000), "The initiation of secondary cracks in compression", Eng. Fract. Mech., 66(2), 187-219. https://doi.org/10.1016/S0013-7944(00)00009-6
  6. Bobet, A. and Einstein, H.H. (1998), "Fracture coalescence in rock-type materials under uniaxial and biaxial compression", J. Rock Mech. Min. Sci., 35(7), 863-889. https://doi.org/10.1016/S0148-9062(98)00005-9
  7. Celestino, S.P., Piltner, R., Monteiro, P.J.M. and Ostertag, C.P. (2001), "Fracture mechanics of marble using a splitting tension test", J. Mater. Civil Eng., 13(6), 407-411. https://doi.org/10.1061/(ASCE)0899-1561(2001)13:6(407)
  8. Chen, G., Kemeny, J. and Harpalani, S. (1992), "Fracture propagation and coalescence in marble plates with pre-cut notches under compression", Proceedings of the Symposium on Fractured and Jointed Rock Mass, Lake Tahoe, California, U.S.A., June.
  9. Chen, G., Zhang, Y., Huang, R., Guo, F. and Zhang, G. (2015), "Failure mechanism of rock bridge based on acoustic emission technique", J. Sens., 1-10.
  10. Cheon, D., Jung, Y., Park, E., Song, W. and Jang, H. (2011), "Evaluation of damage level for rock slopes using acoustic emission technique with waveguides", Eng. Geol., 121(1), 75-88. https://doi.org/10.1016/j.enggeo.2011.04.015
  11. Committee on Fracture Characterization and Fluid Flow (1996), Rock Fractures and Fluid Flow: Contemporary Understanding and Applications, National Academic Press, Washington, U.S.A.
  12. Dyskin, A.V. (2003), "Influence of shape and locations of initial 3-D cracks on their growth in uniaxial compression", Eng. Fract. Mech., 70(15), 2115-2136. https://doi.org/10.1016/S0013-7944(02)00240-0
  13. Deng, Q. and Zhang, P. (1984), "Research on the geometry of shear fracture zones", J. Geophys. Res., 89(B7), 5669-5710. https://doi.org/10.1029/JB089iB07p05669
  14. Dey, T.N. and Wang, C.Y. (1981), "Some mechanisms of microcrack growth and interaction in compressive rock failure", J. Rock Mech. Min. Sci. Geomech. Abstr., 18(3), 199-209. https://doi.org/10.1016/0148-9062(81)90974-8
  15. Einstein, H.H., Veneziano, D., Baecher, G.B. and O'Reillly, K.J. (1983), "The effect of discontinuity persistence on rock slope stability", J. Rock Mech. Min. Sci. Geomech. Abstr., 20(5), 227-236. https://doi.org/10.1016/0148-9062(83)90003-7
  16. Fredrich, J.T., Evans, B. and Wong, T.F. (1990), "Effect of grain size on brittle and semi brittle strength: Implications for micromechanical modelling of failure in compression", J. Geophys. Res., 95(B7), 10907-10920. https://doi.org/10.1029/JB095iB07p10907
  17. Gehle, C. and Kutter, H.K. (2003), "Breakage and shear behavior of intermittent rock joints", J. Rock Mech. Min. Sci., 40(5), 687-700. https://doi.org/10.1016/S1365-1609(03)00060-1
  18. Germanovich, L.N., Carter, B.J., Dyskin, A.V., Ingraffea, A.R. and Lee, K.K. (1996), "Mechanics of 3-D crack growth under compressive loads", Proceedings of the 2nd North American Rock Mechanics Symposium on Rock Mechanics Tools and Techniques, Montreal, Canada, June.
  19. Germanovich, L.N, Salganik, R.L, Dyskin, A.V. and Lee, K.K. (1994), "Mechanisms of brittle fracture of rock with multiple pre-existing cracks in compression", Pure Appl. Geophys., 143(1), 17-149.
  20. Germanovich, L.N., Ring, L.M., Carter, B.J., Ingraffea, A.R., Dyskin, A.V. and Ustinov, K.B. (1995), "Simulation of crack growth and interaction in compression", Proceedings of the 8th International Congress on Rock Mechanics, Tokyo, Japan, September.
  21. Ghazvinian, A., Nikudel, M.R. and Sarfarazi, V. (2007), "Effect of rock bridge continuity and area on shear behavior of joints", Proceedings of the 11th Congress of the International Society of Rock Mechanics, Lisbon, Portugal, July.
  22. Griffth, A.A. (1921), "The phenomena of rupture and flow in solids", Philos. Trans. R. Soc. London Ser. A, 221, 163-198. https://doi.org/10.1098/rsta.1921.0006
  23. Griffith, A.A. (1924), "The theory of rupture", Proceedings of the 1st International Congress on Applied Mechanics, Delft, The Netherlands, April.
  24. Haeri, H. (2015a), "Propagation mechanism of neighboring cracks in rock-like cylindrical specimens under uniaxial compression", J. Min. Sci., 51(3), 487-496. https://doi.org/10.1134/S1062739115030096
  25. Haeri, H. (2015b), "Simulating the crack propagation mechanism of pre-cracked concrete specimens under shear loading conditions", Strength Mater., 47(4), 618-632. https://doi.org/10.1007/s11223-015-9698-z
  26. Haeri, H., Shahriar, K., Marji, M.F. and Moarefvand, P. (2014a), "On the cracks coalescence mechanism and cracks propagation paths in rock-like specimens containing pre-existing random cracks under compression", J. Centr. South Univ., 21(6), 2404-2414. https://doi.org/10.1007/s11771-014-2194-y
  27. Haeri, H., Shahriar, K., Marji, M.F. and Moarefvand, P. (2014b), "Investigating the fracturing process of rock-like Brazilian discs containing three parallel cracks under compressive line loading", Strength Mater., 46(3), 133-148.
  28. Haeri, H., Shahriar, K., Marji, M.F. and Moarefvand, P. (2015a), "On the HDD analysis of micro cracks initiation, propagation and coalescence in brittle substances", Arab. J. Geosci., 8(5), 2841-2852. https://doi.org/10.1007/s12517-014-1290-5
  29. Haeri, H., Marji, M.F. and Shahriar, K. (2015b), "Simulating the effect of disc erosion in TBM disc cutters by a semi-infinite DDM", Arab. J. Geosci., 8(6), 3915-3927. https://doi.org/10.1007/s12517-014-1489-5
  30. Haeri, H., Khaloo, A. and Marji, M.F. (2015c), "Experimental and numerical simulation of the microcracks coalescence mechanism in rock-like materials", Strength Mater., 47(1), 740-754. https://doi.org/10.1007/s11223-015-9711-6
  31. Haeri, H., Khaloo, A. and Marji, M.F. (2015d), "Experimental and numerical analysis of Brazilian discs with multiple parallel cracks", Arab. J. Geosci., 8(8), 5897-5908. https://doi.org/10.1007/s12517-014-1598-1
  32. Haeri, H. and Sarfarazi, V. (2016a), "The deformable multilaminate for predicting the elasto-plastic behavior of rocks", Comput. Concrete, 18(2), 201-214. https://doi.org/10.12989/cac.2016.18.2.201
  33. Haeri, H. and Sarfarazi, V. (2016b), "Numerical simulation of tensile failure of concrete using particle flow code (PFC)", Comput. Concrete, 18(1), 39-51. https://doi.org/10.12989/cac.2016.18.1.039
  34. Hall, S., De Sanctis, F. and Viggiani, G. (2006), "Monitoring fracture propagation in a soft rock (neapolitan tuff) using acoustic emiss ions and digital images", Pure Appl. Geophys., 163(10), 2171-2204. https://doi.org/10.1007/s00024-006-0117-z
  35. Hallbauer, D.K., Wagner, H. and Cook, N.G.W. (1973), "Some observations concerning the microscopic and mechanical behaviour of quartzite specimens in triaxial compression tests", J. Rock Mech. Min. Sci. Geomech. Abstr., 10(6), 713-726. https://doi.org/10.1016/0148-9062(73)90015-6
  36. Hoek, E. and Bieniawski, Z.T. (1984), "Brittle fracture propagation in rock under compresion", J. Fract., 26(4), 276-294. https://doi.org/10.1007/BF00962960
  37. Horii, H. and Nemat-Nasser, S. (1985), "Compression-induced microcrack growth in brittle solids: Axial splitting and shear failure", J. Geophys. Res., 90(B4), 3105-3125. https://doi.org/10.1029/JB090iB04p03105
  38. Horii, S. and Nemat-Nasser, S. (1986), "Brittle failure in compression: splitting, faulting and brittle-ductile transition", Phil. Trans. R. Soc. Lond. A, 319(1549), 337-374. https://doi.org/10.1098/rsta.1986.0101
  39. Hu, B., Zhang, N. and Liu, S. (2009), "Contrastive model test for joint influence on strength and deformation of rock masses", J. Centr. South Univ., 40, 1133-1138.
  40. Huang, M.L., Tang, C.A. and Zhu, W.C. (1999), "Real-time SEM study on rock failure instability under uniaxial compression", J. North Univ., 20, 426-429.
  41. Hussain, M.A., Pu, E.L. and Underwood, J.H. (1974), "Strain energy release rate for a crack under combined model I and mode II", ASTM STP 1974; 560, 2-28.
  42. Ingraffea, A.R. and Heuze, F.E. (1980), "Finite element models for rock fracture mechanics", J. Numer. Anal. Meth. Geomech., 4(1), 25-43. https://doi.org/10.1002/nag.1610040103
  43. Gerges, N., Issa, C. and Fawaz, S. (2015), "Effect of construction joints on the splitting tensile strength of concrete", Case Stud. Constr. Mater., 3, 83-91. https://doi.org/10.1016/j.cscm.2015.07.001
  44. Irwin, G.R. (1957), "Analysis of stresses and strains near the ends of a crack traversing a plate", J. Appl. Mech., 24(3), 361-364.
  45. Jaeger, J.C. (1971), "Friction of rocks and stability of rock slopes", Geotech., 21(2), 97-134. https://doi.org/10.1680/geot.1971.21.2.97
  46. Jamil, S.M. (1999), "Strength of non-persistent rock joints", Ph.D. Dissertation, University of Illinois at Urbana-Champaign, Illinois, U.S.A.
  47. Jansen, D.P., Carlson, S.R., Young, R.P. and Hutchins, D.A. (1993), "Ultrasonic imaging and acoustic emission monitoring of thermally induced microcracks in Lac du Bonnet granite", J. Geophys. Res., 98(B12), 22231-22243. https://doi.org/10.1029/93JB01816
  48. Jennings, J.E. (1970), "A mathematical theory for the calculation of the stability of slopes in open cast mines", Proceedings of the Symposium on the Theoretical Background to the Plannings of Open Pit Mines with Special Reference to Slope Stability, Johannesburg, South Africa, August.
  49. Jiefan, H., Ganglin, C., Yonghong, Z. and Ren, W. (1990), "An experimental study of the strain field development prior to failure of a marble plate under compression", Tectonophys., 175(6), 269-284. https://doi.org/10.1016/0040-1951(90)90142-U
  50. Kemeny, J.M. (1991), "A model for non-linear rock deformation under compression due to subcritical crack growth", J. Rock Mech. Min. Sci. Geomech. Abstr., 28(3), 459-467. https://doi.org/10.1016/0148-9062(91)91121-7
  51. Kemeny, J.M. and Cook, N.G.W. (1987), "Crack models for the failure of rock under compression", Proceedings of the 2nd International Conference on Constitutive Laws for Engineering Materials, Tucson, Arizona, U.S.A., January.
  52. Kim, J. and Taha, M.R. (2014), "Experimental and numerical evaluation of direct tension test for cylindrical concrete specimens", Adv. Civil Eng., 1-8.
  53. Kim, W.J., Lee, J.M., Kim, J.S. and Lee, C.J. (2012), "Measuring high speed crack propagation in concrete fracture test using mechanoluminescent material", Smart Struct. Syst., 10(6), 547-555. https://doi.org/10.12989/sss.2012.10.6.547
  54. Kranz, R.L. (1979), "Crack-crack and crack-pore interactions in stressed granite", J. Rock Mech. Min. Sci. Geomech. Abstr., 16(1), 37-47.
  55. Kranz, R.L. (1983), "Microcracks in rocks: A review", Tectonophys., 100(1-3), 449-480. https://doi.org/10.1016/0040-1951(83)90198-1
  56. Kumar, S. and Barai, S.V. (2012), "Size-effect of fracture parameters for crack propagation in concrete: A comparative study", Comput. Concrete, 9(1), 1-19. https://doi.org/10.12989/cac.2012.9.1.001
  57. Kuntz, M. and Lavallee, P. (1998), "Steady-state flow experiments to visualise the stress field and potential crack trajectories in 2D elastic-brittle cracked media in uniaxial compression", J. Fract., 92(4), 349-357. https://doi.org/10.1023/A:1007537222483
  58. Lajtai, E.Z. (1969a), "Strength of discontinuous rocks in direct shear", Geotech., 19(2), 218-332. https://doi.org/10.1680/geot.1969.19.2.218
  59. Lajtai, E.Z. (1969b), "Shear strength of weakness planes in rock", J. Rock Mech. Min. Sci., 6(5), 499-515. https://doi.org/10.1016/0148-9062(69)90016-3
  60. Lee, H. and Jeon, S. (2011), "An experimental and numerical study of fracture coalescence in pre-cracked specimens under uniaxial compression", J. Sol. Struct., 48(6), 979-999. https://doi.org/10.1016/j.ijsolstr.2010.12.001
  61. Li, Y.P. and Wang, Y.H. (2003), "Analysis on zigzag cracks in rock-like materials under compression", Acta Mech. Sol. Sinic., 24(4), 456-462.
  62. Li, Y., Chen, L. and Wang, Y. (2005), "Experimental research on pre-cracked marble under compression", J. Sol. Struct., 42(9), 2505-2516. https://doi.org/10.1016/j.ijsolstr.2004.09.033
  63. Lin, P., Zhou, W.Y. and Liu, H.Y. (2014), "Experimental study on cracking, reinforcement and overall stability of the xiaowan super-high arch dam", Rock Mech. Rock Eng., 48(2), 819-841. https://doi.org/10.1007/s00603-014-0593-x
  64. Liu, H.Y., Kou, S.Q., Lindqvist, P.A. and Tang, C.A. (2004), "Numerical simulation of shear fracture (mode II) in heterogeneous brittle rock", J. Rock Mech. Min. Sci., 41, 14-19. https://doi.org/10.1016/j.ijrmms.2004.03.013
  65. Mao, H. and Yang, C. (2009), "Analysis of deformation features of slates with structural surfaces", Chin. J. Undergr. Space Eng., 2009(5), 934-938.
  66. Mughieda, O. and Alzoubi, A.K. (2001), "Fracture mechanisms of open offset rock joints under uniaxial loading", M.S. Dissertation, Jordan University of Science and Technology, Irbid, Jordan.
  67. Mughieda, O. and Alzoubi, A. (2004), "Fracture mechanisms of offset rock joints-a laboratory investigation", Geotech. Geol. Eng., 22(4), 545-562. https://doi.org/10.1023/B:GEGE.0000047045.89857.06
  68. Mughieda, O. and Karasneh, I. (2006), "Coalescence of offset rock joints under biaxial landing", Geotech. Geol. Eng., 24(4), 985-999. https://doi.org/10.1007/s10706-005-8352-0
  69. Nemat-Nasser, S. and Horii, H. (1982), "Compression-induced non-planar crack extension with application to splitting, exfoliation and rockburst", J. Geophys. Res., 87(B8), 6805-6821. https://doi.org/10.1029/JB087iB08p06805
  70. Ning, J., Liu, X., Tan, Y., Wang, J. and Tian, C. (2015), "Relationship of box counting of fractured rock mass with Hoek-Brown parameters using particle flow simulation", Geomech. Eng., 9, 619-629. https://doi.org/10.12989/gae.2015.9.5.619
  71. Olsson, W.A. and Pang, S.S. (1976), "Microcrack nucleation in marble", J. Rock Mech. Min. Sci. Geomech. Abstr., 13(2), 53-59.
  72. Panaghi, K., Golshani, A. and Takemura, T. (2015), "Rock failure assessment based on crack density and anisotropy index variations during triaxial loading tests", Geomech. Eng., 9, 793-813. https://doi.org/10.12989/gae.2015.9.6.793
  73. Pang, S. and Jonson, A.M. (1972), "Crack growth and faulting in cylindrical specimens of chelmsford granite", J. Rock Mech. Min. Sci. Geomech. Abstr., 9(1), 37-86. https://doi.org/10.1016/0148-9062(72)90050-2
  74. Papadopoulos, G.A. and Poniridis, P.I. (1989), "Crack initiation under biaxial loading with higher-order approximation", Eng. Fract. Mech., 32(3), 351-360. https://doi.org/10.1016/0013-7944(89)90308-1
  75. Park, N.S. and Jeon, S.W. (2001), "The crack coalescence in rock bridges under uniaxial compression", 3(2), 23-32.
  76. Petit, J. and Barquins, M. (1988), "Can natural faults propagate under mode II conditions?" Tecton., 7(6), 1243-1256. https://doi.org/10.1029/TC007i006p01243
  77. Prudencio, M. and Van Sint Jan, M. (2007), "Strength and failure modes of rock mass models with nonpersistent joints", J. Rock Mech. Min. Sci., 44(6), 890-902. https://doi.org/10.1016/j.ijrmms.2007.01.005
  78. Pu, C., Cao, P. and Zhao, Y. (2010), "Numerical analysis and strength experiment of rock-like materials with multi-fissures under uniaxial compression", Rock Soil Mech., 31(11), 3661-3666.
  79. Reyes, O. (1991), "Experimental study, analytic modeling of compressive fracture in brittle materials", Ph.D. Dissertation, Massachusetts Institute of Technology, Cambridge, U.S.A.
  80. Rudajev, V., Ciz, R., Lokajicek, T. and Vilhelm, J. (2000), "Geological structure, seismic energy release and forecasting of rockburst occurrence", Acta Montan. Ser. A, 16(118), 171-174.
  81. Sagong, M. and Bobet, A. (2000), "Coalescence of multiple flaws in uniaxial compression", Proceedings of the North American Rock Mechanics Symposium: Pacific Rocks, Seattle, Washington, U.S.A., July.
  82. Sagong, M. and Bobet, A. (2002), "Coalescence of multiple flaws in a rock-model material in uniaxial compression", J. Rock Mech. Min. Sci., 39, 229-241. https://doi.org/10.1016/S1365-1609(02)00027-8
  83. Sahouryeh, E. (2002), "Crack growth under biaxial compression", Eng. Fract. Mech., 69, 2187-2198. https://doi.org/10.1016/S0013-7944(02)00015-2
  84. Sammis, C.G. and Ashby, M.F. (1986), "The failure of brittle porous solids under compressive stress states", Acta Metall., 34(3), 511-526. https://doi.org/10.1016/0001-6160(86)90087-8
  85. Sardemir, M. (2016), "Empirical modeling of flexural and splitting tensile strengths of concrete containing fly ash by GEP", Comput. Concrete, 17(4), 489-498. https://doi.org/10.12989/cac.2016.17.4.489
  86. Sarfarazi, V. and Haeri, H. (2016), "The effect of non-persistent joints on sliding direction of rock slopes", Comput. Concrete, 17, 723-737. https://doi.org/10.12989/cac.2016.17.6.723
  87. Sarfarazi, V., Faridi, H.R., Haeri, H. and Schubert, W. (2015), "A new approach for measurement of anisotropic tensile strength of concrete", Adv. Concrete Constr., 3(4), 269-284. https://doi.org/10.12989/acc.2015.3.4.269
  88. Savilahti, T., Nordlund, E. and Stephansson, O. (1990), "Shear box testing and modeling of joint bridge", Proceedings of the International Symposium on Shear Box Testing and Modeling of Joint Bridge Rock Joints, Loen, Norrway, June.
  89. Shah, S.P. (1999a), "Fracture toughness for high-strength concrete", ACI Mater., 87(3), 260-265.
  90. Shah, S.P. (1999b), "Experimental methods for determining fracture process zone and fracture parameters", Eng. Fract. Mech., 35, 3-14.
  91. Shang, J.L., Kong, C.J., Li, T.J. and Zhang, W.Y. (1999), "Observation and study on meso-damage and fracture of rock", J. Exp. Mech., 14(3), 373-383.
  92. Shen, B. (1993), "The mechanics of fracture coalescence in compression experimental study and numerical simulation", Eng. Fract. Mech., 51(1), 73-85. https://doi.org/10.1016/0013-7944(94)00201-R
  93. Shen, B., Stephansson, O., Einstein, H.H. and Ghahreman, B. (1995), "Coalescence of fracture under shear stresses in experiments", J. Geophys. Res., 100(B4), 725-729.
  94. Steif, P.S. (1984), "Crack extension under compressive loading", Eng. Fract. Mech., 20(3), 463-473. https://doi.org/10.1016/0013-7944(84)90051-1
  95. Stimpson, B. (1978), "Failure of slopes containing discontinuous planar joints", Proceedings of the 19th US Symposium on Rock Mechanics, Reno, U.S.A., May.
  96. Takeuchi, K. (1991), "Mixed-mode fracture initiation in granular brittle materials", M.S. Dissertation, Massachusetts Institute of Technology, Cambridge, U.S.A.
  97. Tang, C.A. and Kou, S.Q. (1998), "Fracture propagation and coalescence in brittle materials", Eng. Fract. Mech., 61(3), 311-324. https://doi.org/10.1016/S0013-7944(98)00067-8
  98. Tang, C.A. (1997), "Numerical simulation of progres-sive rock failure and associated seismicity", J. Rock Mech. Min. Sci., 34(2), 249-262. https://doi.org/10.1016/S0148-9062(96)00039-3
  99. Tang, H.D., Zhu, Z.D., Zhu, M.L. and Lin, H.X. (2015), "Mechanical behavior of 3D crack growth in transparent rock-like material containing preexisting flaws under compression", Adv. Mater. Sci. Eng., 1-10.
  100. Tapponnier, P. and Brace, W.F. (1976), "Development of stress-induced micro-cracks in westerly granite", J. Rock Mech. Min. Sci. Geomech. Abstr., 13(4), 103-112. https://doi.org/10.1016/0148-9062(76)91937-9
  101. Wen, W. (2013), "Experimental study on rock-like material with pre-cracks under uniaxial compression", EJGE, 18, 1775-1785.
  102. Weihua, Z., Runqiu, H. and Ming, Y. (2015), "Mechanical and fracture behavior of rock mass with parallel concentrated joints with different dip angle and number based on PFC simulation", Geomech. Eng., 8(6), 757-767. https://doi.org/10.12989/gae.2015.8.6.757
  103. Wong, R.H.C. and Chau, K.T. (1998), "Crack coalescence in a rock-like material containing two cracks", J. Rock Mech. Min. Sci., 35(2), 147-164. https://doi.org/10.1016/S0148-9062(97)00303-3
  104. Wong, R.H.C. and Chau, K.T. (1997), "The coalescence of frictional cracks and the shear zone formation in brittle solids under compressive stresses", J. Rock Mech. Min. Sci., 34(3/4), 366. https://doi.org/10.1016/S1365-1609(97)00075-0
  105. Wong, R.H.C. and Chau, K.T. (1998), "Peak strength of replicated and real rocks containing cracks", Key Eng. Mater., 145, 953-958.
  106. Wong, R.H.C., Chau, K.T., Tang, C.A. and Lin, P. (2001), "Analysis of crack coalescence in rock-like materials containing three flaws-part I: Experimental approach", J. Rock Mech. Min. Sci., 38(7), 909-924. https://doi.org/10.1016/S1365-1609(01)00064-8
  107. Wong, R.H.C., Lin, P., Tang, C.A. and Chau, K.T. (2002), "Creeping damage around an opening in rocklike material containing non-persistent joints", Eng. Fract. Mech., 69(17), 2015-2027. https://doi.org/10.1016/S0013-7944(02)00074-7
  108. Yin, L. and Zhang, P. (2010), "Simulation analysis of rock mass strength affected by dual structural plane", J. Min. Safety Eng., 2010(27), 600-603.
  109. Yang, S.Q. (2015), "An experimental study on fracture coalescence characteristics of brittle sandstone specimens combined various flaws", Geomech. Eng., 8(4), 541-557. https://doi.org/10.12989/gae.2015.8.4.541
  110. Xiang, F., Kulailake, P.H.S.W., Xin, C. and Ping, C. (2015), "Crack initiation stress and strain of jointed rock containing multi-cracks under uniaxial compressive loading: A particle flow code approach", J. Centr. South Univ., 22(2), 638-645. https://doi.org/10.1007/s11771-015-2565-z
  111. Zhang, X. and Wong, L.N.Y. (2012), "Cracking process in rock-like material containing a single flaw under uniaxial compression: A numerical study based on parallel bonded-particle model approach", Rock Mech. Rock Eng., 45(5), 711-737. https://doi.org/10.1007/s00603-011-0176-z
  112. Zhang, X. and Wong, R.H.C. (2013), "Crack initiation, propagation and coalescence in rock-like material containing two flaws: A numerical study based on bonded-particle model approach", Rock Mech. Rock Eng., 46(5), 1001-1021. https://doi.org/10.1007/s00603-012-0323-1
  113. Zhang, X.P. and Wong, L.N.Y. (2012), "Cracking process in rock-like material containing a single flaw under uniaxial compression: A numerical study based on parallel bonded-particle model approach", Rock Mech. Rock Eng., 45(5), 711-737. https://doi.org/10.1007/s00603-011-0176-z
  114. Zhao, Y.H., Liang, H.H., Huang, J.F., Geng, J.D. and Wang, R. (1995), "Development of sub cracks between en echelon fractures in rock plates", Pure Appl. Geophys., 145, 759-773. https://doi.org/10.1007/BF00879599
  115. Zhao, C. (2015), "Analytical solutions for crack initiation on floor-strata interface during mining", Geomech. Eng., 8(2), 237-255. https://doi.org/10.12989/gae.2015.8.2.237
  116. Zhu, W.S., Chen, W.Z. and Shen, J. (1998), "Simulation experiment and fracture mechanism study on propagation of Echelon pattern cracks", Acta Mech. Sol. Sinic., 19, 355-360.

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