Skip to main content
Log in

Elastic–plastic cracking analysis for brittle–ductile rocks using manifold method

  • Original Paper
  • Published:
International Journal of Fracture Aims and scope Submit manuscript

Abstract

In this study, the formation of localized deformation band and failure processes of brittle–ductile materials (coarse and medium marbles) containing pre-existing flaws under various loading conditions are simulated numerically. By incorporating the modified Mohr–Coulomb crack initiation criterion and the crack evolution techniques, the cracking processes, such as crack initiation, propagation and coalescence are successfully modeled by the developed numerical manifold method. According to the results, the development of macro-shear cracks is preceded by the development of localized deformation bands, which are underlain by damage accumulation and material deterioration. The numerical results are comparable to the laboratory test results.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21
Fig. 22
Fig. 23

Similar content being viewed by others

References

  • An XM (2010) Extended numerical manifold methods for engineering failure analysis. Ph.D.Thesis, Nanyang Technology University, Singapore

  • Belytschko T, Black T (1999) Elastic crack growth in finite elements with minimal remeshing. Int J Numer Methods Eng 45(5):601–620

    Article  Google Scholar 

  • Belytschko T, Lu YY, Gu L (1994) Element-free galerkin methods. Int J Numer Methods Eng 37(2):229–256

    Article  Google Scholar 

  • Bobet A (1997) Fracture coalescence in rock materials: experimental observations and numerical predictions. Massachusetts Institute of Technology, Cambridge

  • Bobet A, Einstein HH (1998) Fracture coalescence in rock-type materials under uniaxial and biaxial compression. Int J Rock Mech Min Sci 35(7):863–888

    Article  Google Scholar 

  • Bombolakis EG (1963) Photoelastic stress analysis of crack propagation within a compressive stress field. Ph.D.Thesis. Massachusetts Institute of Technology, Cambridge

  • Bouchard PO, Bay F, Chastel Y (2003) Numerical modelling of crack propagation: automatic remeshing and comparison of different criteria. Comput Methods Appl Mech Eng 192 (35–36):3887–3908

    Google Scholar 

  • Brady B, Brown E (1993) Rock mechanics for underground mining, 2nd edn. Chapman & Hall, London, pp 106–108

  • Chen WF, Han DJ (1988) Plasticity for structural engineers. Springer, New York

    Book  Google Scholar 

  • Chiou YJ, Lee YM, Tsay RJ (2002) Mixed mode fracture propagation by manifold method. Int J Fract 114(4):327–347

    Article  Google Scholar 

  • Cotterell B, Rice JR (1980) Slightly curved or kinked cracks. Int J Fract 16:155–169

    Article  Google Scholar 

  • Cundall PA, Strack ODL (1979) Discrete numerical-model for granular assemblies. Geotechnique 29(1):47–65

    Google Scholar 

  • Donze FV, Bouchez J, Magnier SA (1997) Modeling fracturing in rock blasting. Int J Rock Mech Min Sci 34(8): 1153–1163

    Google Scholar 

  • 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

    Google Scholar 

  • Drucker D, Prager W (1952) Soil mechanics and plastic analysis of limit design. Quat Appl Math 10(2)

  • Erdogan F, Sih SC (1963) On the crack extension in paltes under plane loading and transverse shear. J Basic Eng ASME 85:519–525

    Article  Google Scholar 

  • Huang JF, Chen GG, Zhao YH, Wang R (1990) An experimental-study of the strain field development prior to failure of a marble plate under compression. Tectonophysics 175(1–3): 269–284

    Google Scholar 

  • Hussian MA, PU, Underwood J (1974) Strain energy release rate for a crack under combined mode I and mode II. Fract Anal ASTM STP 560:2–28

  • Ingraffea AR, Heuze FE (1980) Finite-element models for rock fracture-mechanics. Int J Numer Anal Methods Geomech 4(1):25–43

    Article  Google Scholar 

  • Khan SMA, Khraisheh MK (2000) Analysis of mixed mode crack initiation angles under various loading conditions. Eng Fract Mech 67(5):397–419

    Article  Google Scholar 

  • Li SC, Cheng YM (2005) Enriched meshless manifold method for two-dimensional crack modeling. Theor Appl Fract Mech 44(3):234–248

    Article  CAS  Google Scholar 

  • Li S, Cheng Y, Wu YF (2005a) Numerical manifold method based on the method of weighted residues. Comput Mech 35(6):470–480

    Article  Google Scholar 

  • Li YP, Chen LZ, Wang YH (2005b) Experimental research on pre-cracked marble under compression. Int J Solids Struct 42(9–10):2505–2516

    Article  Google Scholar 

  • Ma GW, An XM, Zhang HH, Li LX (2009) Modeling complex crack problems using the numerical manifold method. Int J Fract 156(1):21–35

    Article  Google Scholar 

  • Martinez A (1999) Fracture coalescence in natural rock. M.Sc, Thesis, Massachusetts Institute of Technology, Cambridge

  • Meldelson A (1986) Plastic stress-strain relations. In: Plasticity: theory and application, 2edn. Krieger Publishing, Malabar

  • Melenk JM, Babuska I (1996) The partition of unity finite element method: basic theory and applications. Comput Methods Appl Mech Eng 139(1–4):289–314

    Article  Google Scholar 

  • Ning YJ, An XM, Ma GW (2011) Footwall slope stability analysis with the numerical manifold method. Int J Rock Mech Min Sci 48(6):964–975

    Article  Google Scholar 

  • Park CH, Bobet A (2010) Crack initiation, propagation and coalescence from frictional flaws in uniaxial compression. Eng Fract Mech 77(14):2727–2748

    Article  Google Scholar 

  • Petit J, Barquins M (1988) Can natural faults propagate under mode II conditions? Tectonics 7(6):1246–1265

    Article  Google Scholar 

  • Potyondy DO, Cundall PA (2004) A bonded-particle model for rock. Int J Rock Mech Min Sci 41(8):1329–1364

    Article  Google Scholar 

  • Rabczuk T, Belytschko T (2004) Cracking particles: a simplified meshfree method for arbitrary evolving cracks. Int J Numer Methods Eng 61(13):2316–2343

    Article  Google Scholar 

  • Rabczuk T, Areias PMA, Belytschko T (2007) A simplified mesh-free method for shear bands with cohesive surfaces. Int J Numer Methods Eng 69(5):993–1021

    Google Scholar 

  • Reyes O, Einstein HH (1991) Failure mechanisms of fractured rock- a fracture coalescence model. In: Proceedings—seventh international congress on rock mechanics, vol 1. Rock Mechanics and, Environmental Protection. pp 333–341

  • Shen BT, Stephansson O, Einstein HH, Ghahreman B (1995) Coalescence of fractures under shear stresses in experiments. J Geophys Res Solid Earth 100(B4):5975–5990

    Article  Google Scholar 

  • Shi GH (1991) Manifold method of material analysis. In: Paper presented at the Trans 9th Army conference on applied mathematics and computing. Minesota, Minneaplolis

  • Shi GH (1992) Modeling rock joints and blocks by manifold method. In: Proceedings of the 33th US rock mechanics symposium. San Ta Fe, New Mexico, pp 639–648

  • Shi GH, Goodman RE (1989) Generalization of two-dimensonal discontinuous deformation analysis for forward modeling. Int J Numer Anal Methods Geomech 13:359–380

    Article  Google Scholar 

  • Sih GC (1974) Strain-energy-density factor applied to mixed crack problems. Int J Fract 10:305–321

    Article  Google Scholar 

  • Stefanov YP (2004) Numerical investigation of deformation localization and crack formation in elastic brittle-plastic materials. Int J Fract 128:345–352

    Google Scholar 

  • Strouboulis T, Babuska I, Copps KL (2000a) The design and analysis of the generalized finite element method. Comput Methods Appl Mech Eng 181(1–3):43–69

    Article  Google Scholar 

  • Strouboulis T, Copps K, Babuska I (2000b) The generalized finite element method: an example of its impementaion and illustration of its performance. Int J Numer Anal Methods Geomech 47(8):1401–1417

    Article  Google Scholar 

  • Trädegård A, Nicholas F, Ostlund S (1998) FEM-remeshing technique applied to crack growth problems. Comput Methods Appl Mech Eng 160:115–131

    Article  Google Scholar 

  • Tsay RJ, Chiou YJ, Chuang WL (1999) Crack growth prediction by manifold method. J Eng Mech ASCE 125(8):884–890

    Article  Google Scholar 

  • Vermeer PA, de Borst R (1984) Non-associated plasticity for soils, concrete and rock. Heron 29(3):1–64

    Google Scholar 

  • Wong RHC, Chau KT (1998) Crack coalescence in a rock-like material containing two cracks. Int J Rock Mech Min Sci 35(2):147–164

    Article  Google Scholar 

  • Wong LNY, Einstein HH (2007) Coalescence behavior in Carrara marble and molded gypsum containing artificial flaw pairs under uniaxial compression. In: 1st Canada-U.S. rock mechanics symposium, Vancouver, May 27–31, 2007

  • Wong LNY, Einstein HH (2009a) Crack coalescence in molded gypsum and Carrara marble: part 2-microscopic observations and interpretation. Rock Mech Rock Eng 42(3):513–545

    Google Scholar 

  • Wong LNY, Einstein HH (2009b) Systematic evaluation of cracking behavior in specimens containing single flaws under uniaxial compression. Int J Rock Mech Min Sci 46(2):239–249

    Article  Google Scholar 

  • Wong LNY, Einstein HH (2010) Process zone development associated with cracking processes in Carrara marble. In: The 9th international conference on analysis of discontinuous deformation “New Developments and Applications”. Nanyang Technological University, Singapore, 25–27 November 2009, pp 581-588

  • Wong LNY, Zou C (2012) Cracking processes in rocks under dynamic loading. In: 7th Asian rock mechanics symposium, an ISRM regional symposium, Seoul, Korea, October 15–19, 2012, pp 485–494

  • 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 Sci 38(7):909–924

    Article  Google Scholar 

  • Wu ZJ, Wong LNY (2012) Fricitonal crack initiation and propagtion analysis using the numerical manifold method. Comput Geotech 39:38–53

    Article  CAS  Google Scholar 

  • Yang SQ, Jing HW (2011) Strength failure and crack coalescence behavior of brittle sandstone samples containing a single fissure under uniaxial compression. Int J Fract 168(2):227–250

    Article  Google Scholar 

  • Yang SQ, Jiang YZ, Xu WY, Chen XQ (2008) Experimental investigation on strength and failure behavior of pre-cracked marble under conventional triaxial compression. Int J Solids Struct 45(17):4796–4819

    Article  Google Scholar 

  • Zhang XP, Wong LNY (2012) Cracking processes in rock-like material containg a single flaw under uniaxial compression: a numerical study based on parallel bonded-model approach. Rock Mech Rock Eng 45:711–737

    Google Scholar 

  • Zhang XP, Wong LNY 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 (in press)

  • Zou C, Wong LNY, Cheng Y (2012) The strength and crack behaviour of rock-like gypsum under high strain rate. In: 46th US rock mechanics/ geomechanics symposium, Chicago, IL, June 24–27, 2012. ARMA, pp 312–339

Download references

Acknowledgments

The authors would like to thank Dr Youjun Ning for valuable discussion during the course of this research.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Louis Ngai Yuen Wong.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Wu, Z., Wong, L.N.Y. Elastic–plastic cracking analysis for brittle–ductile rocks using manifold method. Int J Fract 180, 71–91 (2013). https://doi.org/10.1007/s10704-012-9802-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10704-012-9802-3

Keywords

Navigation