Abstract
A continuous-discontinuous cellular automaton method is developed for rock initiation and propagation simulations, in which the level set method, discontinuous enrichment shape functions and discontinuous cellular automaton are combined. No remeshing is needed for crack growth analysis, and all calculations are restricted to cells without an assembled global stiffness matrix. The frictional contact theory is employed to construct the contact model of normal pressure and tangential shear on crack surfaces. A discontinuous cellular automaton updating rule suitable for frictional contact of rock is proposed simultaneously with Newton’s iteration method for nonlinear iteration. Besides, a comprehensive fracturing criterion for brittle rock under compression-shear loading is developed. The accuracy and effectivenesss of the proposed method is proved by numerical simulation.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Griffith, A.A., The phenomena of rapture and flow in solids. Philosophical Transactions of the Royal Society A, 1921, 221: 163–197.
Brace, W.F., Brittle fracture of rocks. In: State of Stress in the Earth’s Crust. (ed Judd). New York, U.S.A.: American Elsevier Publishing Co, 1964: 111–180.
Hoek, E. and Bieniawski, Z.T., Application of the photoelastic coating technique to the study of the stress redistribution associated with plastic flow around notches. The South African Institution of Mechanical Engineering, 1963, 12(8): 222–226.
Jaeger, G.C. and Cook, N.G.W., Foundamental of rock mechanics (2nd Edn). London, U.K.: Chapman and Hall, 1976: 20–55.
Lajtai, E.Z., A theoretical and experimental evaluation of Griffith theory of brittle fracture. Techonophysics, 1971, 11: 129–156.
Bazant, Z.P., Crack band theory for fracture of concrete. Materials and Structures, 1983, 16: 155–177.
Santiago, S.D. and Hilsdorf, H.K., Fracture mechanism of concrete under compressive loads. Cement and Concrete Research, 1973, 3: 363–388.
Blakey, F.A., Mechanism of fracture of concrete. Nature, 1952, 170: 1120.
Hawkes, I. and Mellor, M., Uniaxial testing in rock mechanics laboratories. Engineering Geology, 1970, 4: 177–285.
Chsu, T.T., Slate, G.M., Sturman, G.M. and Winter, G., Microcracking of plain concrete and the shape of the stress-strain curve. ACI Journal proceeding, 1963, 60: 209–224.
Peng, S.D. and Johnson, A.M., Crack growth and faulting in cylindrical specimens of chelmsford granite. International Journal of Rock Mechanics and Mining Sciences & Geomechanics, 1972, 9: 37–86.
Al-Chalabi, M. and Huang, C.L., Stress discontribution within circular cylinders in compression. International Journal of Rock Mechanics and Mining Sciences & Geomechanics, 1974, 11: 45–56.
Lee, H. and Jeon, S., An experimental and numerical study of fracture coalescence in pre-cracked specimens under uniaxial compression. International Journal of Solids and Structures, 2011, 48: 979–999.
Park, C.H. and Bobet, A., Crack initiation, propagation and coalescence from frictional flaws in uniaxial compression. Engineering Fracture Mechanics, 2010, 77: 2727–2748.
Sagong, M. and Bobet, A., Coalescence of multiple flaws in a rock-model material in uniaxial compression. International Journal of Rock Mechanics and Mining Science, 2002, 39: 229–241.
Sih, G.C., Some basic problems in fracture mechanics and new concepts. Journal of Engineering Fracture, 1973, 5: 365–377.
Glucklich, Fracture of plain concrete. Journal of Engineering Mechanics, 1963, 89: 127–138.
Shen, B. and Stephansson, O., Numerical analysis of mixed mode I and II fracture propagation. International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, 1993, 30: 861–867.
Dobroskok, A., Ghassemi, A. and Linkov, A., Extended structural criterion for numerical simulation of crack propagation and coalescence under compressive loads. International Journal of Fracture, 2005, 133: 223–246.
Miao, Y., He, T.G., Yang, Q. and Zheng, J.J., Multi-domain hybrid boundary node method for evaluating top-down crack in asphalt pavements. Engineering Analysis for Boundary Elements, 2010, 34(9): 755–760.
Horii, H. and Nemat-Nasser, S., Brittle failure in compression splitting, faulting and brittle-ductile transition. Philosophical Transactions of the Royal Society A, 1986, 319: 337–374.
Reyes, O. and Einstein, H.H., Failure mechanisms of fractured rock—a fracture coalescence model. In 7th Int. Congress on Rock Mech., 1, ed. Balkema: Wittke W. Rotterdam, 1991, 333–340.
Shen, B. and Stephansson, O., Modification of the G-criterion for fracture propagation subjected to compression. International Journal of Rock Mechanics and Mining Science, 1993, 30: 681–687.
Nemat-Nasser, S. and Horii, H., Compression-induced non-planar crack extension with application to splitting, exfoliation and rockbursts. Journal of Geophysical Research, 1982, B87: 6805–6821.
Zaitsev, Y.V. and Wittmann, F.H., Simulation of crack propagation and failure of concrete. Materials and Structures, 1981, 14: 357–365.
Carpinteri, A., Scavia, C. and Yang, G.P., Microcrack propagation, coalescence and size effects in compression. Engineering Fracture Mechanics, 1996, 54(3): 335–347.
Han, B.C. and Swobada, G.A., A damage mechanics model with wing cracks propagation. In: Computer Methods and Advances in Geomechanics, 2, eds. Siriwardane HJ, Zaman MM. Balkema: Rotterdam, 1993: 1555–1559.
Tang, C.A. and Kou, S.Q., Crack propagation and coalescence in brittle materials under compression. Engineering Fracture Mechanics, 1998, 61: 311–324.
Feng, X.T., Pan, P.Z. and Zhou, H., Simulation of the crack microfracturing process under uniaxial compression using an elasto-plastic cellular automaton. International Journal of Rock Mechanics and Mining Science, 2006, 43: 1091–1108.
Bobet, A. and Einstein, H.H., Numerical modeling of fracture coalescence in a model rock material. International Journal of Fracture, 1998, 92: 221–252.
Wu, Z. J. and Wong, L.N.Y., Frictional crack initiation and propagation analysis using the numerical manifold method. Computers and Geotechnics, 2012, 39: 38–53.
Steen, B.V., Vervoort, A. and Napier, J.A.L., Numerical modeling of fracture initiation and propagation in biaxial tests on rock samples. International Journal of Fracture, 2001, 108: 165–191.
Stolarska, M., Chopp, D.L., Moes, N. and Belytschko, T., Modelling crack growth by level sets in the extended finite element method. International Journal for Numerical Methods in Engineering, 2001, 51: 943–960.
Sethian, J., Evolution, implementation and application of level set and fast marching methods for advancing fronts. Journal of Computational Physics, 2001, 169: 503–555.
Moes, N. and Belytschko, T., Extended finite element method for cohesive crack growth. Engineering Fracture Mechanics, 2002, 69: 813–833.
Shen, C., Dai, S., Yang, J. and Tang, X., Cellular automata for analysis of plane problem in theory of elasticity. Journal of Tsinghua University (Science & Technology), 2001, 41: 35–38 (in Chinese).
Gurdal, Z. and Tatting, T., Cellular automata for design of truss structures with linear and non-linear response. In: Proceedings of 41st AIAA/ASME/ASCE/AHS/ASC Structural Dynamics and Materials Conference, GA: Atlanta, 2000.
Pan, P.Z., Yan, F. and Feng, X.T., Modeling the cracking process of rocks from continuity to discontinuity using a cellular automaton. Computers and Geosciences, 2012, 42: 87–99.
Yan, F., Feng, X.T., Pan, P.Z. and Li, Y.P., A continuous-discontinuous cellular automaton method for regular frictional contact problems. Archive of applied mechanics, 2013, 83(8): 1239–1255.
Rao, Q.H., Sun, Z.Q., Stephansson, O., et al., Shear fracture (Mode II) of brittle rock. International Journal of Rock Mechanics and Mining Science, 2003, 40: 355–375.
Pan, P.Z., Ding, W.X., Feng, X.T., et al., Research on influence of pre-existing crack geometrical and material properties on crack propagation in rocks. Chinese Journal of Rock Mechanics and Engineering, 2008, 27(9): 1882–1889.
Author information
Authors and Affiliations
Corresponding author
Additional information
Project supported by the National Key Technologies R&D Program of China (No. 2013BAB02B01) and the National Natural Science Foundation of China (Nos. 41272349, 41172284 and 51322906).
Rights and permissions
About this article
Cite this article
Yan, F., Feng, X., Pan, P. et al. Rock initiation and propagation simulation under compression-shear loading using continuous-discontinuous cellular automaton method. Acta Mech. Solida Sin. 28, 384–399 (2015). https://doi.org/10.1016/S0894-9166(15)30024-0
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1016/S0894-9166(15)30024-0