Skip to main content
Top
Published in: Rock Mechanics and Rock Engineering 5/2016

12-10-2015 | Original Paper

The 3D Numerical Simulation for the Propagation Process of Multiple Pre-existing Flaws in Rock-Like Materials Subjected to Biaxial Compressive Loads

Authors: J. Bi, X. P. Zhou, Q. H. Qian

Published in: Rock Mechanics and Rock Engineering | Issue 5/2016

Log in

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

General particle dynamics (GPD), which is a novel meshless numerical method, is proposed to simulate the initiation, propagation and coalescence of 3D pre-existing penetrating and embedded flaws under biaxial compression. The failure process for rock-like materials subjected to biaxial compressive loads is investigated using the numerical code GPD3D. Moreover, internal crack evolution processes are successfully simulated using GPD3D. With increasing lateral stress, the secondary cracks keep growing in the samples, while the growth of the wing cracks is restrained. The samples are mainly split into fragments in a shear failure mode under biaxial compression, which is different from the splitting failure of the samples subjected to uniaxial compression. For specimens with macroscopic pre-existing flaws, the simulated types of cracks, the simulated coalescence types and the simulated failure modes are in good agreement with the experimental results.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Literature
go back to reference Aubry R, Idelsohn SR, Oñate E (2005) Particle finite element method in fluid mechanics including thermal convection–diffusion. Comput Struct 83:1459–1475CrossRef Aubry R, Idelsohn SR, Oñate E (2005) Particle finite element method in fluid mechanics including thermal convection–diffusion. Comput Struct 83:1459–1475CrossRef
go back to reference Bardenhagen S, Guilkey J, Roessig K, Brackbill J, Witzel W, Foster J (2001) An improved contact algorithm for the material point method and application to stress propagation in granular material. Comp Model Eng 2:509–522 Bardenhagen S, Guilkey J, Roessig K, Brackbill J, Witzel W, Foster J (2001) An improved contact algorithm for the material point method and application to stress propagation in granular material. Comp Model Eng 2:509–522
go back to reference Beiseel SR, Gerlach CA, Johnson GR (2006) Hypervelocity impact computations with finite elements and meshfree particles. Int J Impact Eng 33:80–90CrossRef Beiseel SR, Gerlach CA, Johnson GR (2006) Hypervelocity impact computations with finite elements and meshfree particles. Int J Impact Eng 33:80–90CrossRef
go back to reference Bobet A, Einstein HH (1998a) Fracture coalescence in rock-type materials under uniaxial and biaxial compression. Int J Rock Mech Min Sci 35:863–888CrossRef Bobet A, Einstein HH (1998a) Fracture coalescence in rock-type materials under uniaxial and biaxial compression. Int J Rock Mech Min Sci 35:863–888CrossRef
go back to reference Bobet A, Einstein HH (1998b) Numerical modeling of fracture coalescence in a model rock material. Int J Fract 92:221–252CrossRef Bobet A, Einstein HH (1998b) Numerical modeling of fracture coalescence in a model rock material. Int J Fract 92:221–252CrossRef
go back to reference Bouchard PO, Baya F, Chastela Y, Tovena I (2000) Crack propagation modelling using an advanced remeshing technique. Comput Methods Appl Mech Eng 189:723–742CrossRef Bouchard PO, Baya F, Chastela Y, Tovena I (2000) Crack propagation modelling using an advanced remeshing technique. Comput Methods Appl Mech Eng 189:723–742CrossRef
go back to reference Chen JK, Beraun JE, Carney TC (1999) A corrective smoothed particle method for boundary value problems in heat conduction. Int J Numer Methods Eng 46:231–252CrossRef Chen JK, Beraun JE, Carney TC (1999) A corrective smoothed particle method for boundary value problems in heat conduction. Int J Numer Methods Eng 46:231–252CrossRef
go back to reference Chen CS, Pan E, Amadei B (1998) Fracture mechanics analysis of cracked discs of anisotropic rock using the boundary element method. Int J Rock Mech Min 35:195–218CrossRef Chen CS, Pan E, Amadei B (1998) Fracture mechanics analysis of cracked discs of anisotropic rock using the boundary element method. Int J Rock Mech Min 35:195–218CrossRef
go back to reference Chen JS, Yoon S, Wang HP, Liu WK (2000) An improved reproducing kernle particle method for nearly incompressibles hyperelastic solids. Comput Methods Appl Mech Eng 181:117–145CrossRef Chen JS, Yoon S, Wang HP, Liu WK (2000) An improved reproducing kernle particle method for nearly incompressibles hyperelastic solids. Comput Methods Appl Mech Eng 181:117–145CrossRef
go back to reference Colagrossi A, Landrini M (2003) Numerical simulation of interfacial flows by smoothed particle hydrodynamics. J Comput Phys 191:448–475CrossRef Colagrossi A, Landrini M (2003) Numerical simulation of interfacial flows by smoothed particle hydrodynamics. J Comput Phys 191:448–475CrossRef
go back to reference Cundall PA, Strack ODL (1979) A discrete numerical model for granular assemblies. Geotechnique 29:47–65CrossRef Cundall PA, Strack ODL (1979) A discrete numerical model for granular assemblies. Geotechnique 29:47–65CrossRef
go back to reference Donze FV, Richefeu V, Magnier SA (2009) Advances in discrete element method applied to soil rock and concrete mechanics. Electron J Geotech Eng 8:1–44 Donze FV, Richefeu V, Magnier SA (2009) Advances in discrete element method applied to soil rock and concrete mechanics. Electron J Geotech Eng 8:1–44
go back to reference Guo Y, Nairn J (2006) Three-dimensional dynamic fracture analysis using the material point method. Comp Model Eng 16:141–155 Guo Y, Nairn J (2006) Three-dimensional dynamic fracture analysis using the material point method. Comp Model Eng 16:141–155
go back to reference Healy D, Jones RR, Holdsworth RE (2006a) New insights into the development of brittle shear fractures from a 3-D numerical model of microcrack interaction. Earth Planet Sci Lett 249:14–28CrossRef Healy D, Jones RR, Holdsworth RE (2006a) New insights into the development of brittle shear fractures from a 3-D numerical model of microcrack interaction. Earth Planet Sci Lett 249:14–28CrossRef
go back to reference Healy D, Jones RR, Holdsworth RE (2006b) Three-dimensional brittle shear fracturing by tensile crack interaction. Nature 439:64–67CrossRef Healy D, Jones RR, Holdsworth RE (2006b) Three-dimensional brittle shear fracturing by tensile crack interaction. Nature 439:64–67CrossRef
go back to reference Hoek E (1990) Estimating Mohr-Coulomb friction and cohesion values from the Hoek–Brown failure criterion. Int J Rock Mech Min 27:227–229CrossRef Hoek E (1990) Estimating Mohr-Coulomb friction and cohesion values from the Hoek–Brown failure criterion. Int J Rock Mech Min 27:227–229CrossRef
go back to reference Hoek E, Brown ET (1980) Empirical strength criterion for rock masses. J Geotech Geoenviron 106(GT9):1013–1036 Hoek E, Brown ET (1980) Empirical strength criterion for rock masses. J Geotech Geoenviron 106(GT9):1013–1036
go back to reference Hoek E, Brown ET (1997) Practical estimate the rock mass strength. Int J Rock Mech Min 34:1165–1186CrossRef Hoek E, Brown ET (1997) Practical estimate the rock mass strength. Int J Rock Mech Min 34:1165–1186CrossRef
go back to reference Huang ML, Wong RHC (2007) Experimental study on propagation and coalescence mechanisms of 3D surface cracks. Chin J Rock Mech Eng 26:1794–1799 Huang ML, Wong RHC (2007) Experimental study on propagation and coalescence mechanisms of 3D surface cracks. Chin J Rock Mech Eng 26:1794–1799
go back to reference Lauterbach B, Gross D (1998) Crack growth in brittle solids under compression. Mech Mater 29:81–92CrossRef Lauterbach B, Gross D (1998) Crack growth in brittle solids under compression. Mech Mater 29:81–92CrossRef
go back to reference Lee H, Jeon S (2011) An experimental and numerical study of fracture coalescence in pre-cracked specimens under uniaxial compression. Int J Solids Struct 48:979–999CrossRef Lee H, Jeon S (2011) An experimental and numerical study of fracture coalescence in pre-cracked specimens under uniaxial compression. Int J Solids Struct 48:979–999CrossRef
go back to reference Liang ZZ, Xing H, Wang SY, Williams DJ, Tang CA (2012) A three-dimensional numerical investigation of the fracture of rock specimens containing a pre-existing surface flaw. Comput Geotech 45:19–33CrossRef Liang ZZ, Xing H, Wang SY, Williams DJ, Tang CA (2012) A three-dimensional numerical investigation of the fracture of rock specimens containing a pre-existing surface flaw. Comput Geotech 45:19–33CrossRef
go back to reference Libersky LD, Petschek AG (1991) Smoothed particle hydrodynamics with strength of materials. In: Trease H, Friits J, Crowley W (eds) Proceedings of the Next Free Lagrange Conference, vol 395. Springer, New York, pp 248–257 Libersky LD, Petschek AG (1991) Smoothed particle hydrodynamics with strength of materials. In: Trease H, Friits J, Crowley W (eds) Proceedings of the Next Free Lagrange Conference, vol 395. Springer, New York, pp 248–257
go back to reference Libersky LD, Petschek AG, Carney TC, Hipp JR, Allahdadi FA (1993) High strain Lagrangian hydrodynamics: a three dimensional SPH code for dynamic material response. J Comput Phys 109:67–75CrossRef Libersky LD, Petschek AG, Carney TC, Hipp JR, Allahdadi FA (1993) High strain Lagrangian hydrodynamics: a three dimensional SPH code for dynamic material response. J Comput Phys 109:67–75CrossRef
go back to reference Liu HY, Kou SQ, Lindqvist PAPA, Tang CA (2004) Numerical simulation of shear fracture (mode II) in heterogeneous brittle rock. Int J Rock Mech Min 41:14–19CrossRef Liu HY, Kou SQ, Lindqvist PAPA, Tang CA (2004) Numerical simulation of shear fracture (mode II) in heterogeneous brittle rock. Int J Rock Mech Min 41:14–19CrossRef
go back to reference Mehra V, Chaturvedi S (2006) High velocity impact of metal sphere on thin metallic plates: a comparative smooth particle hydrodynamics study. J Comput Phys 212:318–337CrossRef Mehra V, Chaturvedi S (2006) High velocity impact of metal sphere on thin metallic plates: a comparative smooth particle hydrodynamics study. J Comput Phys 212:318–337CrossRef
go back to reference Ning YJ, An XM, Ma GW (2011a) Footwall slope stability analysis with the numerical manifold method. Int J Rock Mech Min 48:964–975CrossRef Ning YJ, An XM, Ma GW (2011a) Footwall slope stability analysis with the numerical manifold method. Int J Rock Mech Min 48:964–975CrossRef
go back to reference Ning Y, Yang J, An X, Ma G (2011b) Modelling rock fracturing and blast-induced rock mass failure via advanced discretisation within the discontinuous deformation analysis framework. Comput Geotech 38:40–49CrossRef Ning Y, Yang J, An X, Ma G (2011b) Modelling rock fracturing and blast-induced rock mass failure via advanced discretisation within the discontinuous deformation analysis framework. Comput Geotech 38:40–49CrossRef
go back to reference Paluszny A, Matthai SK (2009) Numerical modeling of discrete multi-crack growth applied to pattern formation in geological brittle media. Int J Solids Struct 46:3383–3397CrossRef Paluszny A, Matthai SK (2009) Numerical modeling of discrete multi-crack growth applied to pattern formation in geological brittle media. Int J Solids Struct 46:3383–3397CrossRef
go back to reference Park CH, Bobet A (2009) Crack coalescence in specimens with open and closed flaws: a comparison. Int J Rock Mech Min 46:819–829CrossRef Park CH, Bobet A (2009) Crack coalescence in specimens with open and closed flaws: a comparison. Int J Rock Mech Min 46:819–829CrossRef
go back to reference Park CH, Bobet A (2010) Crack initiation, propagation and coalescence from frictional flaws in uniaxial compression. Eng Fract Mech 77:2727–2748CrossRef Park CH, Bobet A (2010) Crack initiation, propagation and coalescence from frictional flaws in uniaxial compression. Eng Fract Mech 77:2727–2748CrossRef
go back to reference Pin FD, Idelsohn SR, Oñate E, Aubry R (2007) The ALE/Lagrangian particle finite element method: a new approach to computation of free-surface flows and fluid–object interactions. Comput Fluids 36:27–38CrossRef Pin FD, Idelsohn SR, Oñate E, Aubry R (2007) The ALE/Lagrangian particle finite element method: a new approach to computation of free-surface flows and fluid–object interactions. Comput Fluids 36:27–38CrossRef
go back to reference Randles PW, Libersky LD (1996) Smoothed particle hydrodynamics some recent improvements and applications. Comput Methods Appl Mech Eng 138:375–408CrossRef Randles PW, Libersky LD (1996) Smoothed particle hydrodynamics some recent improvements and applications. Comput Methods Appl Mech Eng 138:375–408CrossRef
go back to reference Sagong M, Bobet A (2002) Coalescence of multiple flaws in a rock-model material in uniaxial compression. Int J Rock Mech Min 39:229–241CrossRef Sagong M, Bobet A (2002) Coalescence of multiple flaws in a rock-model material in uniaxial compression. Int J Rock Mech Min 39:229–241CrossRef
go back to reference Schreyer H, Sulsky D, Zhou S (2002) Modeling delamination as a strong discontinuity with the material point method. Comput Methods Appl Mech Eng 191:2483–2507CrossRef Schreyer H, Sulsky D, Zhou S (2002) Modeling delamination as a strong discontinuity with the material point method. Comput Methods Appl Mech Eng 191:2483–2507CrossRef
go back to reference Shaw A, Reid SR (2009) Applications of SPH with the acceleration correction algorithm in structural impact computations. Curr Sci 97(8):1177–1186 Shaw A, Reid SR (2009) Applications of SPH with the acceleration correction algorithm in structural impact computations. Curr Sci 97(8):1177–1186
go back to reference Shi GH (1991) Manifold method of material analysis. Transactions of the 9th Army Conference on Application of Mathematics and Computing, Minneapolis, USA, pp 57–76 Shi GH (1991) Manifold method of material analysis. Transactions of the 9th Army Conference on Application of Mathematics and Computing, Minneapolis, USA, pp 57–76
go back to reference Shi GH, Goodman RE (1989) Generalization of two-dimensional discontinuous deformation analysis for forward modeling. Int J Numer Anal Methods Geomech 13:359–380CrossRef Shi GH, Goodman RE (1989) Generalization of two-dimensional discontinuous deformation analysis for forward modeling. Int J Numer Anal Methods Geomech 13:359–380CrossRef
go back to reference Strouboulis T, Babuska I, Copps KL (2000a) The design and analysis of the Generalized Finite Element Method. Comput Methods Appl Mech Eng 181:43–69CrossRef Strouboulis T, Babuska I, Copps KL (2000a) The design and analysis of the Generalized Finite Element Method. Comput Methods Appl Mech Eng 181:43–69CrossRef
go back to reference Strouboulis T, Copps K, Babuska I (2000b) The generalized finite element method: an example of its implementation and illustration of its performance. Int J Numer Anal Methods Geomech 47:1401–1417CrossRef Strouboulis T, Copps K, Babuska I (2000b) The generalized finite element method: an example of its implementation and illustration of its performance. Int J Numer Anal Methods Geomech 47:1401–1417CrossRef
go back to reference Sulsky D, Chen Z, Schreyer H (1994) A particle method for history-dependent materials. Comput Methods Appl Mech Eng 118:179–196CrossRef Sulsky D, Chen Z, Schreyer H (1994) A particle method for history-dependent materials. Comput Methods Appl Mech Eng 118:179–196CrossRef
go back to reference Sulsky D, Zhou S, Schreyer H (1995) Application of a particle-in-cell method to solid mechanics. Comput Phys Commun 87:236–252CrossRef Sulsky D, Zhou S, Schreyer H (1995) Application of a particle-in-cell method to solid mechanics. Comput Phys Commun 87:236–252CrossRef
go back to reference Tang CA, Lin P, Wong RHC, Chau KT (2001) Analysis of crack coalescence in rock-like materials containing three flaws—part II: numerical approach. Int J Rock Mech Min 38:925–939CrossRef Tang CA, Lin P, Wong RHC, Chau KT (2001) Analysis of crack coalescence in rock-like materials containing three flaws—part II: numerical approach. Int J Rock Mech Min 38:925–939CrossRef
go back to reference Tsay RJ, Chiou YJ, Chuang WL (1999) Crack growth prediction by manifold method. J Eng Mech 125:884–990CrossRef Tsay RJ, Chiou YJ, Chuang WL (1999) Crack growth prediction by manifold method. J Eng Mech 125:884–990CrossRef
go back to reference Vesga LF, Vallejo LE, Lobo-Guerrero S (2008) DEM analysis of the crack propagation in brittle clays under uniaxial compression tests. Int J Numer Anal Methods Geomech 32:1405–1415CrossRef Vesga LF, Vallejo LE, Lobo-Guerrero S (2008) DEM analysis of the crack propagation in brittle clays under uniaxial compression tests. Int J Numer Anal Methods Geomech 32:1405–1415CrossRef
go back to reference Wang YC, Mora P (2008) Modeling wing crack extension: implications for the Ingredients of Discrete Element Model. Pure Appl Geophys 16:609–620CrossRef Wang YC, Mora P (2008) Modeling wing crack extension: implications for the Ingredients of Discrete Element Model. Pure Appl Geophys 16:609–620CrossRef
go back to reference Wang SY, Sloan SW, Sheng DC et al (2014) Numerical study of failure behaviour of pre-cracked rock specimens under conventional triaxial compression. Int J Solids Struct 51:1132–1148CrossRef Wang SY, Sloan SW, Sheng DC et al (2014) Numerical study of failure behaviour of pre-cracked rock specimens under conventional triaxial compression. Int J Solids Struct 51:1132–1148CrossRef
go back to reference Weibull W (1951) A statistical distribution function of wide applicability. J Appl Mech 18:293–297 Weibull W (1951) A statistical distribution function of wide applicability. J Appl Mech 18:293–297
go back to reference Wong RHC, Chau KT, Tang CA, Lin P (2001) Analysis of crack coalescence in rock-like materials containing three flaws—part I: experimental approach. Int J Rock Mech Min 38:909–924CrossRef Wong RHC, Chau KT, Tang CA, Lin P (2001) Analysis of crack coalescence in rock-like materials containing three flaws—part I: experimental approach. Int J Rock Mech Min 38:909–924CrossRef
go back to reference Wong LNY, Einstein HH (2009a) Crack coalescence in molded gypsum and carrara marble: part 1. Macroscopic observations and interpretation. Rock Mech Rock Eng 42:475–511CrossRef Wong LNY, Einstein HH (2009a) Crack coalescence in molded gypsum and carrara marble: part 1. Macroscopic observations and interpretation. Rock Mech Rock Eng 42:475–511CrossRef
go back to reference Wong LNY, Einstein HH (2009b) Crack coalescence in molded gypsum and carrara marble: part 2—microscopic observations and interpretation. Rock Mech Rock Eng 42:513–545CrossRef Wong LNY, Einstein HH (2009b) Crack coalescence in molded gypsum and carrara marble: part 2—microscopic observations and interpretation. Rock Mech Rock Eng 42:513–545CrossRef
go back to reference Wu ZJ, Wong LNY (2012) Frictional crack initiation and propagation analysis using the numerical manifold method. Comput Geotech 39:38–53CrossRef Wu ZJ, Wong LNY (2012) Frictional crack initiation and propagation analysis using the numerical manifold method. Comput Geotech 39:38–53CrossRef
go back to reference Yang SQ, Jing HW, Wang SY (2012a) Experimental study on the strength, deformability, failure behaviour and spatial acoustic emission distribution of red sandstone under triaxial compression. Rock Mech Rock Eng 45:583–606CrossRef Yang SQ, Jing HW, Wang SY (2012a) Experimental study on the strength, deformability, failure behaviour and spatial acoustic emission distribution of red sandstone under triaxial compression. Rock Mech Rock Eng 45:583–606CrossRef
go back to reference Yang SQ, Yang DS, Jing HW, Li YH, Wang SY (2012b) An experimental study of the fracture coalescence behaviour of brittle sandstone samples containing three fissures. Rock Mech Rock Eng 45:563–582CrossRef Yang SQ, Yang DS, Jing HW, Li YH, Wang SY (2012b) An experimental study of the fracture coalescence behaviour of brittle sandstone samples containing three fissures. Rock Mech Rock Eng 45:563–582CrossRef
go back to reference Yoon J (2007) Application of experimental design and optimization to PFC model calibration in uniaxial compression simulation. Int J Rock Mech Min Sci 44:871–889CrossRef Yoon J (2007) Application of experimental design and optimization to PFC model calibration in uniaxial compression simulation. Int J Rock Mech Min Sci 44:871–889CrossRef
go back to reference York A, Sulsky D, Schreyer H (2000) Fluid-membrane interaction based on the material point method. Int J Numer Methods Eng 48:901–924CrossRef York A, Sulsky D, Schreyer H (2000) Fluid-membrane interaction based on the material point method. Int J Numer Methods Eng 48:901–924CrossRef
go back to reference Yu MH, Zan YW, Zhao J, Yoshimine M (2002) A unified strength criterion for rock material. Int J Rock Mech Min Sci 39:975–989CrossRef Yu MH, Zan YW, Zhao J, Yoshimine M (2002) A unified strength criterion for rock material. Int J Rock Mech Min Sci 39:975–989CrossRef
go back to reference Zhang HH, Li LX, An XM, Ma GW (2010) Numerical analysis of 2-D crack propagation problems using the numerical manifold method. Eng Anal Boundary Elem 34:41–50CrossRef Zhang HH, Li LX, An XM, Ma GW (2010) Numerical analysis of 2-D crack propagation problems using the numerical manifold method. Eng Anal Boundary Elem 34:41–50CrossRef
go back to reference Zhang XP, Wong LNY (2012) Cracking processes 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 45:711–737 Zhang XP, Wong LNY (2012) Cracking processes 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 45:711–737
go back to reference Zhou XP, Cheng H, Feng YF (2014) An experimental study of crack coalescence behaviour in rock-like materials containing multiple flaws under uniaxial compression. Rock Mech Rock Eng 47:1961–1986CrossRef Zhou XP, Cheng H, Feng YF (2014) An experimental study of crack coalescence behaviour in rock-like materials containing multiple flaws under uniaxial compression. Rock Mech Rock Eng 47:1961–1986CrossRef
go back to reference Zhou XP, Bi J, Qian QH (2015a) Numerical simulation of crack growth and coalescence in rock-like materials containing multiple pre-existing flaws. Rock Mech Rock Eng 48(3):1097–1114CrossRef Zhou XP, Bi J, Qian QH (2015a) Numerical simulation of crack growth and coalescence in rock-like materials containing multiple pre-existing flaws. Rock Mech Rock Eng 48(3):1097–1114CrossRef
go back to reference Zhou XP, Zhao Y, Qian QH (2015b) A novel meshless numerical method for modeling progressive failure processes of slopes. Eng Geol 192:139–153CrossRef Zhou XP, Zhao Y, Qian QH (2015b) A novel meshless numerical method for modeling progressive failure processes of slopes. Eng Geol 192:139–153CrossRef
Metadata
Title
The 3D Numerical Simulation for the Propagation Process of Multiple Pre-existing Flaws in Rock-Like Materials Subjected to Biaxial Compressive Loads
Authors
J. Bi
X. P. Zhou
Q. H. Qian
Publication date
12-10-2015
Publisher
Springer Vienna
Published in
Rock Mechanics and Rock Engineering / Issue 5/2016
Print ISSN: 0723-2632
Electronic ISSN: 1434-453X
DOI
https://doi.org/10.1007/s00603-015-0867-y

Other articles of this Issue 5/2016

Rock Mechanics and Rock Engineering 5/2016 Go to the issue