DOI QR코드

DOI QR Code

A review of experimental and numerical investigations about crack propagation

  • Sarfarazi, Vahab (Department of Mining Engineering, Hamedan University of Technology) ;
  • Haeri, Hadi (Department of Mining Engineering, Bafgh Branch, Islamic Azad University)
  • Received : 2016.02.15
  • Accepted : 2016.04.19
  • Published : 2016.08.25

Abstract

A rock mass containing non-persistent joints can only fail if the joints propagate and coalesce through an intact rock bridge. Shear strength of rock mass containing non-persistent joints is highly affected by the both, mechanical behavior and geometrical configuration of non-persistent joints located in a rock mass. Existence of rock joints and rock bridges are the most important factors complicating mechanical responses of a rock mass to stress loading. The joint-bridge interaction and bridge failure dominates mechanical behavior of jointed rock masses and the stability of rock excavations. The purpose of this review paper is to present techniques, progresses and the likely future development directions in experimental and numerical modelling of a non-persistent joint failure behaviour. Such 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. This paper is divided into two sections. In the first part, experimental investigations have been represented followed by a summarized numerical modelling. Experimental results showed failure mechanism of a rock bridge under different loading conditions. Also effects of the number of non-persistent joints, angle between joint and a rock bridge, lengths of the rock bridge and the joint were investigated on the rock bridge failure behaviour. Numerical simulation results are used to validate experimental outputs.

Keywords

References

  1. Aliabadi, M.H. and Brebbia, C.A. (1993), "Advances in boundary element methods for fracture mechanics", Amsterdam: Computational Mechanics Publications, Elsevier.
  2. Altiero, N.Y. and Gioda, G. (1982), "An integral equation approach to fracture propagation in rock", Riv. Ital. Geotecnica, 387-404.
  3. Alzo'ubi (2001), "A fracture mechanisms of open offset rock joints under uniaxial loading", M. Sc. thesis, Jordan University of Science and Technology, Irbid, Jordan.
  4. 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
  5. Bahaaddini, M., Sharrock, G. and Hebblewhie, B.K. (2013), "Numerical investigation of the effect of joint geometrical parameters on the mechanical properties of a non-persistent jointed rock mass under uniaxial compression", Comput. Geotech., 49, 206-225. https://doi.org/10.1016/j.compgeo.2012.10.012
  6. Batzle, M.L., Simmons, G. and Siegfried, R.W. (1980), "Microcrack closure in rocks under stress: direct observation", J. Geophys. Res., 85, 7072-90. https://doi.org/10.1029/JB085iB12p07072
  7. Bi, J., Zhou, X.P. and Qian, Q.H. (2015), "The 3D numerical simulation for the propagation process of multiple pre-existing flaws in rock-like materials subjected to biaxial compressive loads", Rock Mech. Rock Eng., (Published online).
  8. Bieniawski, Z.T. (1967), "Mechanism of brittle fracture of rock Part II-experimental studies", Int. J. Rock Mech. Min. Sci. Geomech. Abstr., 4, 407-23. https://doi.org/10.1016/0148-9062(67)90031-9
  9. Blandford, A.R., Ingraffea, A.R. and Ligget, J.A. (1981), "Two dimensional stress intensity factor computations using the boundary element method", Int. J. Numer. Method. Eng., 17(3), 387-401. https://doi.org/10.1002/nme.1620170308
  10. Bobet, A. (1997), "Fracture coalescence in rock materials: experimental observations and numerical predictions", Sc.D. Thesis, MIT, Cambridge, USA.
  11. 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
  12. Bobet, A. and Einstein, H.H. (1998), "Numerical modeling of fracture coalescence in rock materials", Int. J. Fract., 92(3), 221-52. https://doi.org/10.1023/A:1007460316400
  13. Bobet, A. and Einstein, H.H. (1999), "Fracture coalescence in rock-type materials under uniaxial and biaxial compression", Int. J. Rock Mech. Min. Sci., 35(7), 863-889. https://doi.org/10.1016/S0148-9062(98)00005-9
  14. Carpinteri, A. and Valente, S. (1988), "Size-scale transition from ductile to brittle failure: a dimensional analysis approach", Proceedings of the CNRS-NSF, Workshop on strain localization and size effect due to cracking and damage, Cachan, 447-90.
  15. 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. Civ. Eng., 13(6), 407-411. https://doi.org/10.1061/(ASCE)0899-1561(2001)13:6(407)
  16. Chen, G., Kemeny, J. and Harpalani, S. (1992), "Fracture propagation and coalescence in marble plates with pre-cut notches under compression", Symp. on Fractured and Jointed Rock Mass, Lake Tahoe, CA, 443-448.
  17. Chen, G., Zhang, Y., Huang, R., Guo, F. and Zhang, G. (2015), "Failure mechanism of rock bridge based on acoustic emission technique", J. Sensors, 15, 1-10. https://doi.org/10.1109/JSEN.2014.2366571
  18. 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 (1-2), 75-88. https://doi.org/10.1016/j.enggeo.2011.04.015
  19. Cherepanov, G.P. (1966), "Propagation of cracks in compressed bodies", J. Appl. Math. Mech., (English transl of Prikl Mate Mekh), 30(1), 96-109. https://doi.org/10.1016/0021-8928(66)90060-8
  20. Committee on Fracture Characterization and Fluid Flow et al. (1996), "Rock fractures and fluid flow", Contemporary understanding and applications, Washington, DC: National Academic Press.
  21. De Bremaecker, J.C. and Ferris, M.C. (2004), "Numerical models of shear fracture propagation", Eng. Fract. Mech., 71(15), 2161-2178. https://doi.org/10.1016/j.engfracmech.2003.12.006
  22. 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
  23. Dey, T.N. and Wang, C.Y. (1981), "Some mechanisms of microcrack growth and interaction in compressive rock failure", Int. J. Rock Mech. Min. Sci. Geomech. Abstr., 18(3), 199-209. https://doi.org/10.1016/0148-9062(81)90974-8
  24. Einstein, H.H, Veneziano, D., Baecher, G.B. and O'Reillly, K.J. (1983), "The effect of discontinuity persistence on rock slope stability", Int. J. Rock Mech. Min. Sci. Geomech. Abstr., 20(5), 227-36. https://doi.org/10.1016/0148-9062(83)90003-7
  25. Erdogan, F., Sih, G.C. (1963), "On the crack extension path in plates under plane loading and transverse shear", ASMEJ Basic Eng., 85(4), 516-27.
  26. 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
  27. Gehle, C. and Kutter, H.K. (2003), "Breakage and shear behavior of intermittent rock joints", Int. J. Rock Mech. Min. Sci., 40(5), 687-700. https://doi.org/10.1016/S1365-1609(03)00060-1
  28. 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. Rock mechanics tools and techniques", Proceedings of the Second North American Rock Mechanics Symposium: NARMS '96. Rotterdam: Balkema, 1151-1160.
  29. 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.
  30. Ghazvinian, A., Sarfarazi, V. and Moosavi, S.A. (2010), "Analysis of crack coalescence in rock bridges using neural network", Proceedings of the European Rock Mechanics Symposium, 255-258.
  31. Ghazvinian, A., Sarfarazi, V., Schubert, W. and Blumel, M.A. (2011), "Study of the failure mechanism of planar non-persistent open joints using PFC2D", Rock Mech. Rock Eng. J., 45(5), 677-693.
  32. Griffith, A.A. (1924), "The theory of rupture", Proc.1st Int. Congr. Appl. Mech. Delft, 55-63.
  33. 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
  34. Haeri, H. (2015c), "Influence of the inclined edge notches on the shear-fracture behavior in edge-notched beam specimens", Comput. Concrete, 16(4), 605-623. https://doi.org/10.12989/cac.2015.16.4.605
  35. Haeri, H. (2015d), "Experimental crack analysis of rock-like CSCBD specimens using a higher order DDM", Comput. Concrete, 16(6), 881-896. https://doi.org/10.12989/cac.2015.16.6.881
  36. Haeri, H. (2015e), "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
  37. Haeri, H. (2015f), "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
  38. Haeri, H. and Marji, M.F. (2016b), "Simulating the crack propagation and cracks coalescence underneath TBM disc cutters", Arab. J. Geosci., 9(2), 1-10. https://doi.org/10.1007/s12517-015-2098-7
  39. Haeri, H. and Sarfarazi, V. (2016a), "The effect of micro pore on the characteristics of crack tip plastic zone in concrete", Comput. Concrete, 17(1), 107-12. https://doi.org/10.12989/cac.2016.17.1.107
  40. 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
  41. Haeri, H., Marji, M.F., Shahriar, K. and Moarefvand, P. (2014a), "On the strength and crack propagation process of the pre-cracked rock-like specimens under uniaxial compression", Strength Mater., 46(1), 171-185.
  42. Haeri, H., Marji, M.F., Shahriar, K. and Moarefvand, P. (2014b), "On the crack propagation analysis of rock like Brazilian disc specimens containing cracks under compressive line loading", Latin American J. Solid. Struct., 11(8), 1400-1416. https://doi.org/10.1590/S1679-78252014000800007
  43. Haeri, H., Marji, M.F., Shahriar, K. and Moarefvand, P. (2014c), "A coupled numerical-experimental study of the breakage process of brittle substances", Arab. J. Geosci., 8(2), 809-825 https://doi.org/10.1007/s12517-013-1165-1
  44. Haeri, H., Marji, M.F., Shahriar, K. and Moarefvand, P. (2014d), "On the cracks coalescence mechanism and cracks propagation paths in rock-like specimens containing pre-existing random cracks under compression", J. Central S. Univ., 21(6), 2404-2414. https://doi.org/10.1007/s11771-014-2194-y
  45. Haeri, H., Marji, M.F., Shahriar, K. and Moarefvand, P. (2014e), "Investigating the fracturing process of rock-like Brazilian discs containing three parallel cracks under compressive line loading", Strength Mater., 46(3), 133-148
  46. Haeri, H., Marji, M.F., Shahriar, K. and Moarefvand, P. (2014f), "Experimental and numerical study of crack propagation and coalescence in pre-cracked rock-like disks", Int. J. Rock Mech. Min. Sci., 67, 20-28.
  47. Haeri, H., Marji, M.F., Shahriar, K. 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
  48. Hall, S.A., De Sanctis, F. and Viggiani, G. (2006), "Monitoring fracture propagation in a soft rock (Neapolitan Tuff) using acoustic emissions and digital images", Pure Appl. Geophys., 163(10), 2171-2204. https://doi.org/10.1007/s00024-006-0117-z
  49. Hallbauer, D.K., Wagner, H.N.G.W. and Cook, N.G.W. (1973), "Some observations concerning the microscopic and mechanical behaviour of quartzite specimens in stiff, triaxial compression tests", Int. J. Rock Mech. Min. Sci. Geomech. Abstr., 10(6), 713-726. https://doi.org/10.1016/0148-9062(73)90015-6
  50. Hoek, E. and Bieniawski, Z.T. (1984), "Brittle fracture propagation in rock under compression", Int. J. Fract., 26(4), 276-294. https://doi.org/10.1007/BF00962960
  51. Horii, H. and Nemat-Nasser, S. (1985), "Compression-induced microcrack growth in brittle solids: axial splitting and shear failure", J. Geophys. Res., 90(B4), 3. https://doi.org/10.1029/JB090iS01p00003
  52. Horii, S. and Nemat-Nasser, S. (1986), "Brittle failure in compression: splitting, faulting and brittle-ductile transition", Phil. Trans. R. Soc. Lond., 319(1549), 337-74. https://doi.org/10.1098/rsta.1986.0101
  53. Hu, B., Zhang, N. and Liu, S. (2009), "Contrastive model test for joint influence on strength and deformation of rock masses", J. Central S. Univ. (Sci. Tech.), 40, 1133-1138.
  54. Hussain, M.A. and Pu, E.L. (1974), "Underwood JH, Strain energy release rate for a crack under combined model I and mode II", 560, 2-28.
  55. Ibraheem, O.F., Bakar, B.H.A. and Johari, I. (2015), "Behavior and crack development of fiber-reinforced concrete spandrel beams under combined loading: an experimental study", Struct. Eng. Mech., 54(1), 1-17. https://doi.org/10.12989/sem.2015.54.1.001
  56. Ingraffea, A.R. and Heuze, F.E. (1980), "Finite element models for rock fracture mechanics", Int. J. Numer. Anal. Meth. Geomech., 4(1), 25-43. https://doi.org/10.1002/nag.1610040103
  57. Irwin, G.R. (1957), "Analysis of stresses and strains near the ends of a crack traversing a plate", J. Appl. Mech., 24, 361-364.
  58. 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
  59. Jamil, S.M. (1999), "Strength of non-persistent rock joints", Ph. D. thesis, University of Illinois at Urbana-Champaign, IL, U.S.A.
  60. 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. Solid Earth, 98(B12), 22231-22243. https://doi.org/10.1029/93JB01816
  61. Jennings, J.E. (1970), "A mathematical theory for the calculation of the stability of slopes in open cast mines", Planning Open Pit Mines, Proceedings of the Symposium on the Theoretical Background to the Plannings of Open Pit Mines with Special Reference to Slope Stability, Johannesburg, 87-102.
  62. 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
  63. Kemeny, J. (2005), "Time-dependent drift degradation due to the progressive failure of rock bridges along discontinuities", Int. J. Rock Mech. Min. Sci., 42(1), 35-46. https://doi.org/10.1016/j.ijrmms.2004.07.001
  64. Kemeny, J.M. (1991), "A model for non-linear rock deformation under compression due to subcritical crack growth", Int. J. Rock Mech. Min. Sci. Geomech. Abstr., 28(3), 459-467. https://doi.org/10.1016/0148-9062(91)91121-7
  65. Kemeny, J.M. and Cook, N.G.W. (1987), "Crack models for the failure of rock under compression", Proc. 2nd Int. Conf. Constitutive Laws for Eng. Materials, 2, 879-887.
  66. Kranz, R.L. (1979), "Crack-crack and crack-pore interaction s in stressed granite", Int. J. Rock Mech. Min. Sci. Geomech. Abstr., 16, 37-47.
  67. Kranz, R.L., Microcracks in rocks: A review. Tectonophysics , 1983, 100, 449-480. https://doi.org/10.1016/0040-1951(83)90198-1
  68. Kulatilake, P.H.S.W., Malama, B. and Wang, J. (2001), "Physical and particle flow modeling of jointed rock block behaviour under uniaxial loading", Int. J. Rock Mech. Min. Sci., 38(5), 641-657. https://doi.org/10.1016/S1365-1609(01)00025-9
  69. 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", Int. J. Fract., 92(4), 349-357. https://doi.org/10.1023/A:1007537222483
  70. Lajtai, E.Z. (1969b), "Shear strength of weakness planes in rock", Int. J. Rock Mech. Min. Sci., 6(5), 499-515. https://doi.org/10.1016/0148-9062(69)90016-3
  71. 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
  72. Li, C., Stephansson, O. and Savilahti, T. (1990), "Behavior of rock joints and rock bridges in shear testing", Proceedings of the International Symposium on Rock Joints, 259-266.
  73. Li, Y., Chen, L. and Wang, Y. (2005), "Experimental research on pre-cracked marble under compression", Int. J. Solid. Struct., 42(9), 2505-2516. https://doi.org/10.1016/j.ijsolstr.2004.09.033
  74. Li, Y.P. and Wang, Y.H. (2003), "Analysis on zigzag cracks in rock-like materials under compression", Acta Mech. Solida Sinica, 24(4), 456-462.
  75. Lin, P., Wong, R.H.C., Chau, K.T. and Tang, C.A. (2000), "Multi-crack coalescence in rock-like material under uniaxial and biaxial loading", Key Eng. Mater., 183, 809-14.
  76. 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", Int. J. Rock Mech. Min. Sci., 41, 3. https://doi.org/10.1016/S1365-1609(03)00025-X
  77. Mao, H. and Yang, C. (2009), "Analysis of deformation features of slates with structural surfaces", Chinese J. Underg. Space Eng., 5, 934-938.
  78. Mingli, H., Chunan, T. and Wancheng, Z. (1999), "Real-time SEM study on rock failure instability under uniaxial compression", J. Northeastern Univ. Natural Sci., 20, 429-432.
  79. Mughieda, O. and Alzoubi, A. (2004), "Fracture mechanisms of offset rock joints-A laboratory investigation", Geotech. Geol. Eng., 22, 545-562. https://doi.org/10.1023/B:GEGE.0000047045.89857.06
  80. Mughieda, O. and Karasneh, I. (2006), "Coalescence of offset rock joints under", Geotech. Geol. Eng., 24, 985-999. https://doi.org/10.1007/s10706-005-8352-0
  81. Mughieda, O. and Omar, M.T. (2008), "Stress analysis for rock mass failure with offset joints", Geotech. Geol. Eng., 26(5), 543-552. https://doi.org/10.1007/s10706-008-9188-1
  82. Mughieda, V. and Khawaldeh, I. (2004), Scale effect on engineering properties of open non-persistent rock joints under uniaxial loading, Bolgesel Kaya Mekanig i Sempozyumu/ ROCKMEC '2004-VIIth Regional Rock Mechanics Symposium, Sivas, Turkiye.
  83. Nemat-Nasser, S. and Horii, H. (1982), "Compression-induced non-planar crack extension with application to splitting, exfoliation and rockburst", J. Geophy. Res., 87(B8), 6805-6821. https://doi.org/10.1029/JB087iB08p06805
  84. Olsson,W.A. and Pang, S.S. (1976), "Microcrack nucleation in marble", Int. J. Rock Mech. Min. Sci. Geomech. Abstr., 13(2), 53-59. https://doi.org/10.1016/0148-9062(76)90704-X
  85. Pan, B., Gao, Y. and Zhong, Y. (2014), "Theoretical analysis of overlay resisting crack propagation in old cement concrete pavement", Struct. Eng. Mech., 52(4), 829-841. https://doi.org/10.12989/sem.2014.52.4.829
  86. 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
  87. Peng, S. and Johnson, A.M. (1972), "Crack growth and faulting in cylindrical specimens of Chelmsford granite", Int. J. Rock Mech. Min. Sci. Geomech. Abstr., 9(1), 37-86, Pergamon. https://doi.org/10.1016/0148-9062(72)90050-2
  88. Petit, J. P. and Barquins, M. (1988), "Can natural faults propagate under mode II conditions?", Tecton., 7(6), 1243-1256. https://doi.org/10.1029/TC007i006p01243
  89. Potyondy, D.O. and Cundall, P.A. (2004), "A bonded-particle model for rock", Int. J. Rock Mech. Min. Sci., 41(8), 1329-1364. https://doi.org/10.1016/j.ijrmms.2004.09.011
  90. Prudencio, M. and Van Sint Jan, M. (2007), "Strength and failure modes of rock mass models with nonpersistent joints", Int. J. Rock Mech. Min. Sci., 44(6), 890-902. https://doi.org/10.1016/j.ijrmms.2007.01.005
  91. Pu, C.Z., Cao, P., Zhao Y.L., Zhang, X.Y., Yi, Y.L. and Lit, Y.K. (2010), "Numerical analysis and strength experiment of rock-like materials with multi-fissures under uniaxial compression", J. Rock Soil Mech., 11, 051.
  92. Reyes, O. (1991), "Experimental study, analytic modeling of compressive fracture in brittle materials", Ph.D.Thesis, Massachusetts Institute of Technology, Cambridge.
  93. Reyes, O. and Einstein, H.H. (1991), "Failure mechanism of fractured rock fracture coalescence model", Proceeding of the Seventh Congress of the ISRM, I, 333-40.
  94. Rudajev, V., Vilhelm, J. and Lokajicek, T. (2000), "Laboratory studies of acoustic emission prior to uniaxial compressive rock failure", Int. J. Rock Mech. Min. Sci., 37(4), 699-704. https://doi.org/10.1016/S1365-1609(99)00126-4
  95. Sagong, M. and Bobet, A. (2000), "Coalescence of multiple flaws in uniaxial compression", Proceedings of the North American Rock Mechanics Symposium: Pacific Rocks, 1203-1210.
  96. Sagong, M. and Bobet, A. (2002), "Coalescence of multiple flaws in a rock-model material in uniaxial compression", Int. J. Rock Mech. Min. Sci., 39(2), 229-241. https://doi.org/10.1016/S1365-1609(02)00027-8
  97. 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
  98. Sarfarazi, V., Ghazvinian, A., Schubert, W., Blumel, M. and Nejati, H.R. (2014), "Numerical simulation of the process of fracture of Echelon rock joints", Rock Mech. Rock Eng., 45(5), 677-693. https://doi.org/10.1007/s00603-012-0233-2
  99. Savilahti, T., Nordlund, E. and Stephansson, O. (1990), "Shear box testing and modeling of joint bridge", Proceedings of international symposium on shear box testing and modeling of joint bridge Rock Joints, 295-300, Norway.
  100. Scavia, C. (1999), "The displacement discontinuity method for the analysis of rock structures: a fracture mechanic", Aliabadi MH, editor. Fracture of Rock. Boston: WIT press, Computational Mechanics Publications, 39-82.
  101. Scavia, C. and Castelli, M. (1996), "Analysis of the propagation of natural discontinuities in rock bridges", Barla G, ed. EUROCK'98. Rotterdam: Balkema, 445-51.
  102. Scholtes, L. and Donze, F. (2012), "Modelling progressive failure in fractured rock masses using a 3D discrete element method", Int. J. Rock Mech. Min. Sci., 52(2012), 18-30. https://doi.org/10.1016/j.ijrmms.2012.02.009
  103. Shah, S.P. (1999a), "Fracture toughness for high-strength concrete", ACI Mater., 87, 260-265.
  104. Shah, S.P. (1999b), "Experimental methods for determining fracture process zone and fracture parameters", Eng. Fract. Mech., 35, 3-14.
  105. 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, 373-383.
  106. 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
  107. Shen, B. and Stephansson, O. (1990), "Cyclic loading characteristics of joints and rock bridges in a jointed rock specimen", Proceedings of the International Symposium on Rock Joints, 725-729.
  108. Shen, B. and Stephansson, O. (1994), "Modification of the g-criterion for crack propagation subjected to compression", Eng. Fract. Mech., 47(2), 177-89. https://doi.org/10.1016/0013-7944(94)90219-4
  109. Shen, B., Stephansson, O., Einstein, H.H. and Ghahreman, B. (1995), "Coalescence of fracture under shear stresses in experiments", J. Geophys. Res., 100, 725-729.
  110. Sih, G.C. (1974), "Strain-energy-density factor applied to mixed mode crack problems", Int. J. Fract., 10(3), 305-321. https://doi.org/10.1007/BF00035493
  111. 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
  112. Stimpson, B. (1978), "Failure of slopes containing discontinuous planar joints", Proceedings of the 19th US Symposium on Rock Mechanics, Stateline, Nevada, 296-302.
  113. Takeuchi, K. (1991), "Mixed-mode fracture initiation in granular brittle materials", M.S. Thesis, Massachusetts Institute of Technology, Cambridge, MA.
  114. Tang, C. (1997), "Numerical simulation of progressive rock failure and associated seismicity", Int. J. Rock Mech. Min. Sci., 34(2), 249-261. https://doi.org/10.1016/S0148-9062(96)00039-3
  115. Tang, C.A. and Kou, S.Q. (1998), "Crack propagation and coalescence in brittle materials under compression", Eng. Fract. Mech., 61(3), 311-324. https://doi.org/10.1016/S0013-7944(98)00067-8
  116. 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
  117. Tapponnier, P. and Brace, W.F. (1976), "Development of stress-induced micro-cracks in Westerly granite", Int. J. Rock Mech. Min. Sci. Geomech. Abstr., 13(4), 103-12. https://doi.org/10.1016/0148-9062(76)91937-9
  118. Tien, Y.M., Kuo, M.C. and Juang, C.H. (2006), "An experimental investigation of the failure mechanism of simulated transversely isotropic rocks", Int. J. Rock Mech. Min. Sci., 43(8), 1163-1181. https://doi.org/10.1016/j.ijrmms.2006.03.011
  119. Vasarhelyi, B. and Bobet, A. (2000), "Modeling of crack initiation, propagation and coalescence in uniaxial compression", Rock Mech. Rock Eng., 33(2), 119-39. https://doi.org/10.1007/s006030050038
  120. Wang, S., Huang, R., Ni, P., Gamage, R.P. and Zhang, M. (2013), "Fracture behavior of intact rock using acoustic emission: experimental observation and realistic modeling", Geotech. Test. J., 36(6), 1-12.
  121. Wang, S.Y., Sloan, S.W., Sheng, D.C. and Tang, C.A. (2015), "3D numerical analysis of crack propagation of heterogeneous notched rock under uniaxial tension", Techtonophys., 16, 30042-7.
  122. Wang, S.Y., Sloan, S.W., Sheng, D.C., Yang, S.Q. and Tang, C.A. (2014), "Numerical study of failure behaviour of pre-cracked rock specimens under conventional triaxial compression", Int. J. Solid. Struct., 51(5), 1132-1148. https://doi.org/10.1016/j.ijsolstr.2013.12.012
  123. Wang, S.Y., Sloan, S.W., Tang, C.A. and Zhu, W.C. (2012b), "A numerical investigation of the failure mechanism around tunnels in transversely isotropic rock masses", Tunnel. Underg. Space Tech., 32, 231-244. https://doi.org/10.1016/j.tust.2012.07.003
  124. Wong, R.H.C., Chau, K.T., Tsoi, P.M. and Tang, C.A. (1999), "Pattern of coalescence of rock bridge between two joints under shear testing", Proceedings of the 9th International Congress on Rock Mechanics, 735-738.
  125. Wong, R.H.C. (1997), "Failure mechanisms, peak strength of natural rocks and rock-like solids containing frictional cracks", Ph.D. Thesis, The Hong Kong Polytechnic University, Hong Kong.
  126. 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", Int. J. Rock Mech. Min. Sci., 34(3), 366. https://doi.org/10.1016/S1365-1609(97)00075-0
  127. Wong, R.H.C. and Chau, K.T. (1998), "Crack coalescence in a rock-like material containing two cracks", Int. J. Rock Mech. Min. Sci., 35(2), 147-164. https://doi.org/10.1016/S0148-9062(97)00303-3
  128. Wong, R.H.C. and Chau, K.T. (1998), "Peak strength of replicated and real rocks containing cracks", Key Eng. Mater., 145, 953-8.
  129. 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", Int. J. Rock Mech. Min. Sci., 38(7), 909-924. https://doi.org/10.1016/S1365-1609(01)00064-8
  130. 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", Int. J. Rock Mech. Min. Sci., 38, 909-24. https://doi.org/10.1016/S1365-1609(01)00064-8
  131. Wong, R.H.C., Leung, W.L. and Wang, S.W. (2001), :Shear strength study on rock-like models containing arrayed open joints. Rock mechanics in the national interest", Elsworth D, Tinucci JP, Heasley KA, Eds. Swets & Zeitlinger Lisse, 843-9.
  132. Wong, R.H.C., Lin, P., Chau, K.T. and Tang, C.A. (2000), "The effects of confining compression on fracture coalescence in rock-like material", Key Eng. Mater., 183, 857-62.
  133. 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
  134. Wong, R.H.C., Tang, C.A., Chau, K.T. and Lin, P. (2002), "Splitting failure in brittle rocks containing preexisting flaws under uniaxial compression", Eng. Fract. Mech., 69(17), 1853-1871. https://doi.org/10.1016/S0013-7944(02)00065-6
  135. Wong, T.F. (1982), "Micromechanics of faulting in Westerly granite", Int. J. Rock Mech. Min. Sci. Geomech. Abstr., 19(2), 49-64. https://doi.org/10.1016/0148-9062(82)91631-X
  136. 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. Cent. South Univ., 22(2), 638-645. https://doi.org/10.1007/s11771-015-2565-z
  137. Yang, S., Jing, H. and Wang, S. (2012), "Experimental investigation on the strength, deformability, failure behaviour and acoustic emission locations of red sandstone under triaxial compression", Rock Mech. Rock Eng., 45(4), 583-606. https://doi.org/10.1007/s00603-011-0208-8
  138. Yin, L. and Zhang, P. (2010), "Simulation analysis of rock mass strength affected by dual structural plane", J. Min. Safety Eng., 4, 600-603.
  139. Zhang, F., Wang, B., Chen, Z., Wang, X. and Jia, Z. (2008), "Rock bridge slice element method in slope stability analysis based on multi-scale geological structure mapping", J. Cent. S. Univ. Tech., 15(2), 131-137. https://doi.org/10.1007/s11771-008-0448-2
  140. Zhang, H.Q., Zhao, Z.Y., Tang, C.A. and Song, L. (2006), "Numerical study of shear behavior of intermittent rock joints with different geometrical parameters", Int. J. Rock Mech. Min. Sci., 43(5), 802-816. https://doi.org/10.1016/j.ijrmms.2005.12.006
  141. 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", J. Rock Mech. Rock Eng., 46(5), 1001-1021. https://doi.org/10.1007/s00603-012-0323-1
  142. Zhang, X., 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
  143. Zhao, Y. and Wan, W. (2013), "An experimental and simulation analysis on fracture of rock bridge under shear pressure", 18, 419-426.
  144. 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, 759-73. https://doi.org/10.1007/BF00879599
  145. Zhu, W., Li, S., Wong, R.H.C., Chau, K.T. and Xu, J. (2004), "A study of fracture mechanism and shear strength of rock bridges through analytical and model-testing methods", Key Eng. Mater., 261-263, 225-230. https://doi.org/10.4028/www.scientific.net/KEM.261-263.225
  146. Zhu, W.S., Chen, W.Z. and Shen, J. (1998), "Simulation experiment and fracture mechanism study on propagation of Echelon pattern cracks", Acta Mech. Solida Sinica, 19, 355-360.

Cited by

  1. Simulating Tensile and Compressive Failure Process of Concrete with a User-defined Bonded-Particle Model vol.12, pp.1, 2018, https://doi.org/10.1186/s40069-018-0292-1
  2. Simulating damage evolution and fracture propagation in sandstone containing a preexisting 3-D surface flaw under uniaxial compression pp.03639061, 2019, https://doi.org/10.1002/nag.2908
  3. Theoretical and numerical analysis of stress and stress intensity factor in bi-material vol.10, pp.1, 2019, https://doi.org/10.1108/IJSI-08-2018-0048
  4. Computer modeling of crack propagation in concrete retaining walls: A case study vol.19, pp.5, 2016, https://doi.org/10.12989/cac.2017.19.5.509
  5. Simulation of crack initiation and propagation in three point bending test using PFC2D vol.66, pp.4, 2016, https://doi.org/10.12989/sem.2018.66.4.453
  6. PFC3D simulation of the effect of particle size on the single edge-notched rectangle bar in bending test vol.68, pp.4, 2016, https://doi.org/10.12989/sem.2018.68.4.497
  7. Numerical simulations of fracture shear test in anisotropy rocks with bedding layers vol.7, pp.4, 2016, https://doi.org/10.12989/acc.2019.7.4.241
  8. Effects of seepage and weak interlayer on the failure modes of surrounding rock: model tests and numerical analysis vol.6, pp.9, 2016, https://doi.org/10.1098/rsos.190790
  9. Analysis of notch depth and loading rate effects on crack growth in concrete by FE and DIC vol.24, pp.6, 2016, https://doi.org/10.12989/cac.2019.24.6.527
  10. Experimental Study of the Mechanism of TBM Disk Cutter Penetration in Mixed-Faced Grounds under Confining Pressure vol.48, pp.3, 2016, https://doi.org/10.1520/jte20190563
  11. Fracture Analysis in Brittle Sandstone by Digital Imaging and AE Techniques: Role of Flaw Length Ratio vol.32, pp.5, 2020, https://doi.org/10.1061/(asce)mt.1943-5533.0003151
  12. Numerical analysis of fracturing behavior in fully-graded concrete with oversized aggregates from mesoscopic perspective vol.253, pp.None, 2016, https://doi.org/10.1016/j.conbuildmat.2020.119184
  13. Investigation into Macro- and Microcrack Propagation Mechanism of Red Sandstone under Different Confining Pressures Using 3D Numerical Simulation and CT Verification vol.2021, pp.None, 2016, https://doi.org/10.1155/2021/2871687
  14. Analysis of the crack propagation rules and regional damage characteristics of rock specimens vol.24, pp.3, 2016, https://doi.org/10.12989/gae.2021.24.3.215
  15. Compressive-shear fracture model of the phase-field method coupled with a modified Hoek-Brown criterion vol.229, pp.2, 2016, https://doi.org/10.1007/s10704-021-00546-7