Skip to main content
Top
Published in: Rock Mechanics and Rock Engineering 12/2020

26-08-2020 | Original Paper

An Experimental and Numerical Study on the Influence of Filling Materials on Double-Crack Propagation

Authors: Xiaoying Zhuang, Shuwei Zhou

Published in: Rock Mechanics and Rock Engineering | Issue 12/2020

Log in

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

search-config
loading …

Abstract

Filling materials such as clay or sand widely exist in natural rock joints and work as weak bonds between the joint surfaces. The fillings affect rock deformation and failure behavior, and show different influences in terms of single crack or multiple cracks. While most of the literature have focused on unfilled cracks in brittle materials, this study aims to investigate various filling materials on the crack behavior, e.g., initiation, secondary cracks and peak strength. In this paper, the crack propagation in rock-like specimens with double-filled and unfilled cracks are investigated experimentally and numerically. Uniaxial compression tests were conducted and the experimental observations indicate that the peak stress and first crack initiation stress of the specimens vary with different geometries and different filling materials, while the crack initiation location and the pattern of crack coalescence show similar behavior between filled and unfilled cracks. In parallel to the experimental tests, numerical simulations were carried out using a modified phase field model (PFM) to complement the experiments and provide a new perspective. The PFM is found to produce consistent stress–strain curve, strength, and crack patterns with those observed in the experimental tests for both unfilled and filled cracks.

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!

Appendix
Available only for authorised users
Literature
go back to reference Ambati M, Gerasimov T, De Lorenzis L (2015) A review on phase-field models of brittle fracture and a new fast hybrid formulation. Comput Mech 55(2):383–405 Ambati M, Gerasimov T, De Lorenzis L (2015) A review on phase-field models of brittle fracture and a new fast hybrid formulation. Comput Mech 55(2):383–405
go back to reference Amor H, Marigo J-J, Maurini C (2009) Regularized formulation of the variational brittle fracture with unilateral contact: Numerical experiments. J Mech Phys Solids 57(8):1209–1229 Amor H, Marigo J-J, Maurini C (2009) Regularized formulation of the variational brittle fracture with unilateral contact: Numerical experiments. J Mech Phys Solids 57(8):1209–1229
go back to reference Belytschko T, Black T (1999) Elastic crack growth in finite elements with minimal remeshing. Int J Numer Methods Eng 45(5):601–620 Belytschko T, Black T (1999) Elastic crack growth in finite elements with minimal remeshing. Int J Numer Methods Eng 45(5):601–620
go back to reference Bilgen C, Weinberg K (2019) On the crack-driving force of phase-field models in linearized and finite elasticity. Comput Methods Appl Mech Eng 353:348–372 Bilgen C, Weinberg K (2019) On the crack-driving force of phase-field models in linearized and finite elasticity. Comput Methods Appl Mech Eng 353:348–372
go back to reference Bobet A, Einstein H (1998a) Fracture coalescence in rock-type materials under uniaxial and biaxial compression. Int J Rock Mech Min Sci 35(7):863–888 Bobet A, Einstein H (1998a) Fracture coalescence in rock-type materials under uniaxial and biaxial compression. Int J Rock Mech Min Sci 35(7):863–888
go back to reference Bobet A, Einstein HH (1998b) Numerical modeling of fracture coalescence in a model rock material. Int J Fract 92(3):221 Bobet A, Einstein HH (1998b) Numerical modeling of fracture coalescence in a model rock material. Int J Fract 92(3):221
go back to reference Borden MJ, Verhoosel CV, Scott MA, Hughes TJ, Landis CM (2012) A phase-field description of dynamic brittle fracture. Comput Methods Appl Mech Eng 217:77–95 Borden MJ, Verhoosel CV, Scott MA, Hughes TJ, Landis CM (2012) A phase-field description of dynamic brittle fracture. Comput Methods Appl Mech Eng 217:77–95
go back to reference Bouchard P-O, Bay F, Chastel Y, Tovena I (2000) Crack propagation modelling using an advanced remeshing technique. Comput Methods Appl Mech Eng 189(3):723–742 Bouchard P-O, Bay F, Chastel Y, Tovena I (2000) Crack propagation modelling using an advanced remeshing technique. Comput Methods Appl Mech Eng 189(3):723–742
go back to reference Bourdin B, Francfort GA, Marigo J-J (2000) Numerical experiments in revisited brittle fracture. J Mech Phys Solids 48(4):797–826 Bourdin B, Francfort GA, Marigo J-J (2000) Numerical experiments in revisited brittle fracture. J Mech Phys Solids 48(4):797–826
go back to reference Bourdin B, Francfort GA, Marigo J-J (2008) The variational approach to fracture. J Elast 91(1–3):5–148 Bourdin B, Francfort GA, Marigo J-J (2008) The variational approach to fracture. J Elast 91(1–3):5–148
go back to reference Brace W, Bombolakis E (1963) A note on brittle crack growth in compression. J Geophys Res 68(12):3709–3713 Brace W, Bombolakis E (1963) A note on brittle crack growth in compression. J Geophys Res 68(12):3709–3713
go back to reference Bryant EC, Sun W (2018) A mixed-mode phase field fracture model in anisotropic rocks with consistent kinematics. Comput Methods Appl Mech Eng 342:561–584 Bryant EC, Sun W (2018) A mixed-mode phase field fracture model in anisotropic rocks with consistent kinematics. Comput Methods Appl Mech Eng 342:561–584
go back to reference Cheng Z, Wang Z, Luo Z (2019) Dynamic fracture analysis for shale material by peridynamic modelling. Comput Model Eng Sci 118(3):509–527 Cheng Z, Wang Z, Luo Z (2019) Dynamic fracture analysis for shale material by peridynamic modelling. Comput Model Eng Sci 118(3):509–527
go back to reference Clayton JD (2019) Computational modeling of dual-phase ceramics with finsler-geometric phase field mechanics. Comput Model Eng Sci 120(2):333–350 Clayton JD (2019) Computational modeling of dual-phase ceramics with finsler-geometric phase field mechanics. Comput Model Eng Sci 120(2):333–350
go back to reference Cook NG (1965) The failure of rock. Int J Rock Mech Min Sci Geomech Abstr 2:389–403 Cook NG (1965) The failure of rock. Int J Rock Mech Min Sci Geomech Abstr 2:389–403
go back to reference Deb D, Das KC (2009) Extended finite element method (xfem) for analysis of cohesive rock joint. J Sci Indus Res 68:575–583 Deb D, Das KC (2009) Extended finite element method (xfem) for analysis of cohesive rock joint. J Sci Indus Res 68:575–583
go back to reference Donze F, Bouchez J, Magnier S (1997) Modeling fractures in rock blasting. Int J Rock Mech Min Sci 34(8):1153–1163 Donze F, Bouchez J, Magnier S (1997) Modeling fractures in rock blasting. Int J Rock Mech Min Sci 34(8):1153–1163
go back to reference Fakhimi A, Gharahbagh EA (2011) Discrete element analysis of the effect of pore size and pore distribution on the mechanical behavior of rock. Int J Rock Mech Min Sci 48(1):77–85 Fakhimi A, Gharahbagh EA (2011) Discrete element analysis of the effect of pore size and pore distribution on the mechanical behavior of rock. Int J Rock Mech Min Sci 48(1):77–85
go back to reference Feng D-C, Wu J-Y (2018) Phase-field regularized cohesive zone model (czm) and size effect of concrete. Eng Fract Mech 197:66–79 Feng D-C, Wu J-Y (2018) Phase-field regularized cohesive zone model (czm) and size effect of concrete. Eng Fract Mech 197:66–79
go back to reference Fowell R, Hudson J, Xu C, Zhao X et al (1995) Suggested method for determining mode i fracture toughness using cracked chevron notched brazilian disc (ccnbd) specimens. Int J Rock Mech Min Sci Geomech Abstr 7:322A Fowell R, Hudson J, Xu C, Zhao X et al (1995) Suggested method for determining mode i fracture toughness using cracked chevron notched brazilian disc (ccnbd) specimens. Int J Rock Mech Min Sci Geomech Abstr 7:322A
go back to reference Hoek E, Bieniawski Z (1965) Brittle fracture propagation in rock under compression. Int J Fract Mech 1(3):137–155 Hoek E, Bieniawski Z (1965) Brittle fracture propagation in rock under compression. Int J Fract Mech 1(3):137–155
go back to reference Hosseini-Tehrani P, Hosseini-Godarzi A, Tavangar M (2005) Boundary element analysis of stress intensity factor ki in some two-dimensional dynamic thermoelastic problems. Eng Anal Bound Elem 29(3):232–240 Hosseini-Tehrani P, Hosseini-Godarzi A, Tavangar M (2005) Boundary element analysis of stress intensity factor ki in some two-dimensional dynamic thermoelastic problems. Eng Anal Bound Elem 29(3):232–240
go back to reference Lajtai E (1974) Brittle fracture in compression. Int J Fract 10(4):525–536 Lajtai E (1974) Brittle fracture in compression. Int J Fract 10(4):525–536
go back to reference Li H, Wong LNY (2012) Influence of flaw inclination angle and loading condition on crack initiation and propagation. Int J Solids Struct 49(18):2482–2499 Li H, Wong LNY (2012) Influence of flaw inclination angle and loading condition on crack initiation and propagation. Int J Solids Struct 49(18):2482–2499
go back to reference Li Q, Li Z, Xu X (2020) Experimental study for the effect of fillings on properties of brittle rock containing two parallel flaws. Geotech Geol Eng 38:3643–3651 Li Q, Li Z, Xu X (2020) Experimental study for the effect of fillings on properties of brittle rock containing two parallel flaws. Geotech Geol Eng 38:3643–3651
go back to reference Liu Z, Menouillard T, Belytschko T (2011) An xfem/spectral element method for dynamic crack propagation. Int J Fract 169(2):183–198 Liu Z, Menouillard T, Belytschko T (2011) An xfem/spectral element method for dynamic crack propagation. Int J Fract 169(2):183–198
go back to reference Lu X, Wu W-L (2006) A subregion drbem formulation for the dynamic analysis of two-dimensional cracks. Math Comput Modell 43(1–2):76–88 Lu X, Wu W-L (2006) A subregion drbem formulation for the dynamic analysis of two-dimensional cracks. Math Comput Modell 43(1–2):76–88
go back to reference Meng F, Zhou H, Wang Z, Zhang L, Kong L, Li S, Zhang C (2017) Influences of shear history and infilling on the mechanical characteristics and acoustic emissions of joints. Rock Mech Rock Eng 50(8):2039–2057 Meng F, Zhou H, Wang Z, Zhang L, Kong L, Li S, Zhang C (2017) Influences of shear history and infilling on the mechanical characteristics and acoustic emissions of joints. Rock Mech Rock Eng 50(8):2039–2057
go back to reference Miehe C, Hofacker M, Welschinger F (2010) A phase field model for rate-independent crack propagation: Robust algorithmic implementation based on operator splits. Comput Methods Appl Mech Eng 199(45–48):2765–2778 Miehe C, Hofacker M, Welschinger F (2010) A phase field model for rate-independent crack propagation: Robust algorithmic implementation based on operator splits. Comput Methods Appl Mech Eng 199(45–48):2765–2778
go back to reference Moës N, Dolbow J, Belytschko T (1999) A finite element method for crack growth without remeshing. Int J Numer Methods Eng 46(1):131–150 Moës N, Dolbow J, Belytschko T (1999) A finite element method for crack growth without remeshing. Int J Numer Methods Eng 46(1):131–150
go back to reference Mughieda O, Alzo’ubi AK (2004) Fracture mechanisms of offset rock joints-a laboratory investigation. Geotech Geol Eng 22(4):545–562 Mughieda O, Alzo’ubi AK (2004) Fracture mechanisms of offset rock joints-a laboratory investigation. Geotech Geol Eng 22(4):545–562
go back to reference Nikravesh S, Gerstle W (2018) Improved state-based peridynamic lattice model including elasticity, plasticity and damage. Comput Model Eng Sci 116(3):323–347 Nikravesh S, Gerstle W (2018) Improved state-based peridynamic lattice model including elasticity, plasticity and damage. Comput Model Eng Sci 116(3):323–347
go back to reference Palmström A, Sharma V, Saxena K (2001) In-situ characterization of rocks. A.A. Balkema Publishers, Tokyo, pp 1–40 Palmström A, Sharma V, Saxena K (2001) In-situ characterization of rocks. A.A. Balkema Publishers, Tokyo, pp 1–40
go back to reference Park C, Bobet A (2009) Crack coalescence in specimens with open and closed flaws: a comparison. Int J Rock Mech Min Sci 46(5):819–829 Park C, Bobet A (2009) Crack coalescence in specimens with open and closed flaws: a comparison. Int J Rock Mech Min Sci 46(5):819–829
go back to reference Pereira JP (1997) Rolling friction and shear behaviour of rock discontinuities filled with sand. Int J Rock Mech Min Sci 34(3–4):244–e1 Pereira JP (1997) Rolling friction and shear behaviour of rock discontinuities filled with sand. Int J Rock Mech Min Sci 34(3–4):244–e1
go back to reference Shahani A, Fasakhodi MA (2009) Finite element analysis of dynamic crack propagation using remeshing technique. Mater Des 30(4):1032–1041 Shahani A, Fasakhodi MA (2009) Finite element analysis of dynamic crack propagation using remeshing technique. Mater Des 30(4):1032–1041
go back to reference Shen B, Stephansson O (1993) Numerical analysis of mixed mode i and mode ii fracture propagation. Int J Rock Mech Min Sci Geomech Abstr 30:861–867 Shen B, Stephansson O (1993) Numerical analysis of mixed mode i and mode ii fracture propagation. Int J Rock Mech Min Sci Geomech Abstr 30:861–867
go back to reference Shen B, Stephansson O (1994) Modification of the g-criterion for crack propagation subjected to compression. Eng Fract Mech 47(2):177–189 Shen B, Stephansson O (1994) Modification of the g-criterion for crack propagation subjected to compression. Eng Fract Mech 47(2):177–189
go back to reference Shen B, Stephansson O, Einstein HH, Ghahreman B (1995) Coalescence of fractures under shear stresses in experiments. J Geophys Res Solid Earth 100(B4):5975–5990 Shen B, Stephansson O, Einstein HH, Ghahreman B (1995) Coalescence of fractures under shear stresses in experiments. J Geophys Res Solid Earth 100(B4):5975–5990
go back to reference Talamini B, Mao Y, Anand L (2018) Progressive damage and rupture in polymers. J Mech Phys Solids 111:434–457 Talamini B, Mao Y, Anand L (2018) Progressive damage and rupture in polymers. J Mech Phys Solids 111:434–457
go back to reference Trädegård A, Nilsson F, Östlund S (1998) Fem-remeshing technique applied to crack growth problems. Comput Methods Appl Mech Eng 160(1–2):115–131 Trädegård A, Nilsson F, Östlund S (1998) Fem-remeshing technique applied to crack growth problems. Comput Methods Appl Mech Eng 160(1–2):115–131
go back to reference Wen P, Aliabadi M, Rooke D (1998) Cracks in three dimensions: a dynamic dual boundary element analysis. Comput Methods Appl Mech Eng 167(1–2):139–151 Wen P, Aliabadi M, Rooke D (1998) Cracks in three dimensions: a dynamic dual boundary element analysis. Comput Methods Appl Mech Eng 167(1–2):139–151
go back to reference Wong L, Einstein H (2009) Crack coalescence in molded gypsum and carrara marble: part 1. macroscopic observations and interpretation. Rock Mech Rock Eng 42(3):475–511 Wong L, Einstein H (2009) Crack coalescence in molded gypsum and carrara marble: part 1. macroscopic observations and interpretation. Rock Mech Rock Eng 42(3):475–511
go back to reference Wong R, Chau K, Tang C, 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 Wong R, Chau K, Tang C, 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
go back to reference Wong RH, Chau K (1998) Crack coalescence in a rock-like material containing two cracks. Int J Rock Mech Min Sci 35(2):147–164 Wong RH, Chau K (1998) Crack coalescence in a rock-like material containing two cracks. Int J Rock Mech Min Sci 35(2):147–164
go back to reference Wu J-Y (2017) A unified phase-field theory for the mechanics of damage and quasi-brittle failure. J Mech Phys Solids 103:72–99 Wu J-Y (2017) A unified phase-field theory for the mechanics of damage and quasi-brittle failure. J Mech Phys Solids 103:72–99
go back to reference Wu Z, Wong LNY (2012) Frictional crack initiation and propagation analysis using the numerical manifold method. Comput Geotech 39:38–53 Wu Z, Wong LNY (2012) Frictional crack initiation and propagation analysis using the numerical manifold method. Comput Geotech 39:38–53
go back to reference Yang S, Yang D, Jing H, Li Y, Wang S (2012) An experimental study of the fracture coalescence behaviour of brittle sandstone specimens containing three fissures. Rock Mech Rock Eng 45(4):563–582 Yang S, Yang D, Jing H, Li Y, Wang S (2012) An experimental study of the fracture coalescence behaviour of brittle sandstone specimens containing three fissures. Rock Mech Rock Eng 45(4):563–582
go back to reference Yang S-Q (2011) Crack coalescence behavior of brittle sandstone samples containing two coplanar fissures in the process of deformation failure. Eng Fract Mech 78(17):3059–3081 Yang S-Q (2011) Crack coalescence behavior of brittle sandstone samples containing two coplanar fissures in the process of deformation failure. Eng Fract Mech 78(17):3059–3081
go back to reference Yin P, Wong R, Chau K (2014) Coalescence of two parallel pre-existing surface cracks in granite. Int J Rock Mech Min Sci 68:66–84 Yin P, Wong R, Chau K (2014) Coalescence of two parallel pre-existing surface cracks in granite. Int J Rock Mech Min Sci 68:66–84
go back to reference Yonghong Z (2004) Mini-crack development from a cemented fracture in marble specimen under uniaxial compression. Chin J Rock Mech Eng 23:2504–2509 Yonghong Z (2004) Mini-crack development from a cemented fracture in marble specimen under uniaxial compression. Chin J Rock Mech Eng 23:2504–2509
go back to reference Yu Y, Xia P, Yang C (2018) Form finding and collapse analysis of cable nets under dynamic loads based on finite particle method. Comput Model Sci 117(1):73–89 Yu Y, Xia P, Yang C (2018) Form finding and collapse analysis of cable nets under dynamic loads based on finite particle method. Comput Model Sci 117(1):73–89
go back to reference Zhang H, Li L, An X, Ma G (2010) Numerical analysis of 2-d crack propagation problems using the numerical manifold method. Eng Anal Bound Elem 34(1):41–50 Zhang H, Li L, An X, Ma G (2010) Numerical analysis of 2-d crack propagation problems using the numerical manifold method. Eng Anal Bound Elem 34(1):41–50
go back to reference Zhang B, Li S-C, Zhang D-F, Li M-T, Shao D-L (2012) Uniaxial compression mechanical property test, fracture and damage analysis of similar material of jointed rock mass with filled cracks. Rock Soil Mech 33(6):1647–1652 Zhang B, Li S-C, Zhang D-F, Li M-T, Shao D-L (2012) Uniaxial compression mechanical property test, fracture and damage analysis of similar material of jointed rock mass with filled cracks. Rock Soil Mech 33(6):1647–1652
go back to reference Zhang X-P, 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(5):711–737 Zhang X-P, 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(5):711–737
go back to reference Zhang X, Sloan SW, Vignes C, Sheng D (2017) A modification of the phase-field model for mixed mode crack propagation in rock-like materials. Comput Methods Appl Mech Eng 322:123–136 Zhang X, Sloan SW, Vignes C, Sheng D (2017) A modification of the phase-field model for mixed mode crack propagation in rock-like materials. Comput Methods Appl Mech Eng 322:123–136
go back to reference Zhou S, Zhuang X, Rabczuk T (2018a) A phase-field modeling approach of fracture propagation in poroelastic media. Eng Geol 240:189–203 Zhou S, Zhuang X, Rabczuk T (2018a) A phase-field modeling approach of fracture propagation in poroelastic media. Eng Geol 240:189–203
go back to reference Zhou S, Zhuang X, Zhu H, Rabczuk T (2018b) Phase field modelling of crack propagation, branching and coalescence in rocks. Theoret Appl Fract Mech 96:174–192 Zhou S, Zhuang X, Zhu H, Rabczuk T (2018b) Phase field modelling of crack propagation, branching and coalescence in rocks. Theoret Appl Fract Mech 96:174–192
go back to reference Zhou S, Zhuang X, Rabczuk T (2019) Phase field modeling of brittle compressive-shear fractures in rock-like materials: A new driving force and a hybrid formulation. Comput Methods Appl Mech Eng 355:729–752 Zhou S, Zhuang X, Rabczuk T (2019) Phase field modeling of brittle compressive-shear fractures in rock-like materials: A new driving force and a hybrid formulation. Comput Methods Appl Mech Eng 355:729–752
go back to reference Zhu H, Wang Q, Zhuang X (2016) A nonlinear semi-concurrent multiscale method for fractures. Int J Impact Eng 87:65–82 Zhu H, Wang Q, Zhuang X (2016) A nonlinear semi-concurrent multiscale method for fractures. Int J Impact Eng 87:65–82
go back to reference Zhuang X, Chun J, Zhu H (2014a) A comparative study on unfilled and filled crack propagation for rock-like brittle material. Theoret Appl Fract Mech 72:110–120 Zhuang X, Chun J, Zhu H (2014a) A comparative study on unfilled and filled crack propagation for rock-like brittle material. Theoret Appl Fract Mech 72:110–120
go back to reference Zhuang X, Zhu H, Augarde C (2014b) An improved meshless shepard and least squares method possessing the delta property and requiring no singular weight function. Comput Mech 53(2):343–357 Zhuang X, Zhu H, Augarde C (2014b) An improved meshless shepard and least squares method possessing the delta property and requiring no singular weight function. Comput Mech 53(2):343–357
Metadata
Title
An Experimental and Numerical Study on the Influence of Filling Materials on Double-Crack Propagation
Authors
Xiaoying Zhuang
Shuwei Zhou
Publication date
26-08-2020
Publisher
Springer Vienna
Published in
Rock Mechanics and Rock Engineering / Issue 12/2020
Print ISSN: 0723-2632
Electronic ISSN: 1434-453X
DOI
https://doi.org/10.1007/s00603-020-02220-1

Other articles of this Issue 12/2020

Rock Mechanics and Rock Engineering 12/2020 Go to the issue