3D Numerical Study on the Growth and Coalescence of Pre-existing Flaws in Rocklike Materials Subjected to Uniaxial Compression
Publication: International Journal of Geomechanics
Volume 16, Issue 4
Abstract
A novel, meshless numerical method, called general particle dynamics (GPD), is proposed to simulate the initiation, propagation, and coalescence of three-dimensional (3D), pre-existing penetrating and embedded flaws as well as size effects and large deformations of rock materials. On the basis of the nonlinear unified strength criterion, an elastic–brittle–plastic damage model was developed to reflect the initiation, growth, and coalescence of the 3D flaws and the macrofailure of rocklike materials by tracing the propagation of the cracks. Then, growth paths of cracks were captured through the sequence of such damaged particles. In this paper, the GPD code is applied to simulate the macrofailure, large deformation, and size effects of the heterogeneous rocklike materials. The present numerical simulations focus on the effects of sample sizes, the nonoverlapping length and types of flaws on the failure, and the complete stress–strain curves of the rocklike materials. The initiation, propagation, and coalescence processes of the wing cracks, the antiwing cracks, the oblique secondary cracks, the out-of-plane shear cracks, and the quasi-coplanar shear crack in a rocklike sample subjected to uniaxial compression is numerically simulated using GPD3D. The numerical results indicate that the nonoverlapping lengths and types of flaws significantly influence the coalescence types. The numerical results are in good agreement with the experimental results. It is proven that the GPD3D can adequately simulate the failure processes, large deformation, and size effects of the rocklike materials.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
This work was supported by the National Natural Science Foundation of China (51325903 and 51279218), Project 973 (2014CB046903), Natural Science Foundation Project of CQ CSTC (cstc2013kjrc-ljrccj0001 and cstc2013jcyjys0005), and Research fund by the Doctoral Program of Higher Education of China (20130191110037).
References
Aubry, R., Idelsohn, S. R., and Oñate, E. (2005). “Particle finite element method in fluid-mechanics including thermal convection-diffusion.” Comput. Struct., 83(17–18), 1459–1475.
Bardenhagen, S. G., Guilkey, J. E., Roessig, K. M., Brackbill, J. U., Witzel, W. M., and Foster, J. C. (2001). “An improved contact algorithm for the material point method and application to stress propagation in granular material.” Comp. Model. Eng. Sci., 2(4), 509–522.
Beissel, S. R., Gerlach, C. A., and Johnson, G. R. (2006). “Hypervelocity impact computations with finite elements and meshfree particles.” Int. J. Impact Eng., 33(1–12), 80–90.
Belytschko, T., and Black, T. (1999). “Elastic crack growth in finite elements with minimal remeshing.” Int. J. Numer. Methods Eng., 45(5), 601–620.
Bobet, A. (2000). “The initiation of secondary cracks in compression.” Eng. Fract. Mech., 66(2), 187–219.
Bobet, A., and Einstein, H. 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., and Einstein, H. H. (1998b). “Numerical modeling of fracture coalescence in a model rock material.” Int. J. Fract., 92(3), 221–252.
Bouchard, P. O., Bay, F., Chastel, Y., and Tovena, I. (2000). “Crack propagation modelling using an advanced remeshing technique.” Comput. Methods Appl. Mech. Eng., 189(3), 723–742.
Chen, C.-S., Pan, E., and Amadei, B. (1998). “Fracture mechanics analysis of cracked discs of anisotropic rock using the boundary element method.” Int. J. Rock Mech. Min. Sci., 35(2), 195–218.
Chen, J. K., Beraun, J. E., and Carney, T. C. (1999). “A corrective smoothed particle method for boundary value problems in heat conduction.” Int. J. Numer. Methods Eng., 46(2), 231–252.
Chen, J.-S., Yoon, S., Wang, H.-P., and Liu, W. K. (2000). “An improved reproducing kernel particle method for nearly incompressible finite elasticity.” Comput. Methods Appl. Mech. Eng., 181(1–3), 117–145.
Colagrossi, A., and Landrini, M. (2003). “Numerical simulation of interfacial flows by smoothed particle hydrodynamics.” J. Comput. Phys., 191(2), 448–475.
Cundall, P. A., and Strack, O. D. L. (1979). “A discrete numerical model for granular assemblies.” Géotechnique, 29(1), 47–65.
Del Pin, F., Idelsohn, S., Oñate, E., and 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(1), 27–38.
Donzé, F. V., Bouchez, J., and Magnier, S. A. (1997). “Modeling fractures in rock blasting.” Int. J. Rock Mech. Min. Sci., 34(8), 1153–1163.
Donzé, F. V., Richefeu, V., and Magnier, S.-A. (2009). “Advances in discrete element method applied to soil, rock and concrete mechanics.” Electron. J. Geotech. Eng., 8, 1–44.
Dyskin, A. V., Germanovich, L. N., and Ustinov, K. B. (1999). “A 3-D model of wing crack growth and interaction.” Eng. Fract. Mech., 63(1), 81–110.
Dyskin, A. V., Jewell, R. J., Joer, H., Sahouryeh, E., and Ustinov, K. B. (1994). “Experiments on 3-D crack growth in uniaxial compression.” Int. J. Fract., 65(4), R77–R83.
Guinea, G. V., Planas, J., and Elices, M. (1992). “Measurement of the fracture energy using three-point bend tests: Part 1—Influence of experimental procedures.” Mater. Struct., 25(4), 212–218.
Guo, Y. J., and Nairn, J. A. (2006). “Three-dimensional dynamic fracture analysis using the material point method.” Comp. Model Eng. Sci., 1(1), 11–45.
Guo, Y. S., Wong, R. H. C., and Zhu, W. S. (2007). “Study on fracture pattern of open surface-flaw in gabbro.” Chin. J. Rock Mech. Eng., 26(3), 525–531.
Hoek, E. (1983). “Strength of jointed rock masses.” Géotechnique, 33(3), 187–223.
Hoek, E. (1990). “Estimating Mohr–Coulomb friction and cohesion values from the Hoek–Brown failure criterion.” Int. J. Rock Mech. Min. Sci. Geomech. Abstr., 27(3), 227–229.
Hoek, E., and Brown, E. T. (1980). “Empirical strength criterion for rock masses.” J. Geotech. Geoenviron., 106(9), 1013–1035.
Hoek, E., and Brown, E. T. (1997). “Practical estimates of rock mass strength.” Int. J. Rock Mech. Min. Sci., 34(8), 1165–1186.
Lauterbach, B., and Gross, D. (1998). “Crack growth in brittle solids under compression.” Mech. Mater., 29(2), 81–92.
Lee, H., and Jeon, S. (2011). “An experimental and numerical study of fracture coalescence in pre-cracked specimens under uniaxial compression.” Int. J. Solids Struct., 48(6), 979–999.
Liang, Z. Z., Xing, H., Wang, S. Y., Williams, D. J., and Tang, C. A. (2012). “A three-dimensional numerical investigation of the fracture of rock specimens containing a pre-existing surface flaw.” Comput. Geotech., 45, 19–33.
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(5), 14–19.
Mehra, V., and Chaturvedi, S. (2006). “High velocity impact of metal sphere on thin metallic plates: A comparative smooth particle hydrodynamics study.” J. Comput. Phys., 212(1), 318–337.
Ning, Y., Yang, J., An, X., and Ma, G. (2011a). “Modelling rock fracturing and blast-induced rock mass failure via advanced discretisation within the discontinuous deformation analysis framework.” Comput. Geotech., 38(1), 40–49.
Ning, Y. J., An, X. M., and Ma, G. W. (2011b). “Footwall slope stability analysis with the numerical manifold method.” Int. J. Rock Mech. Min. Sci., 48(6), 964–975.
Park, C. H., and 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. H., and Bobet, A. (2010). “Crack initiation, propagation and coalescence from frictional flaws in uniaxial compression.” Eng. Fract. Mech., 77(14), 2727–2748.
Potyondy, D. O., and Cundall, P. A. (2004). “A bonded-particle model for rock.” Int. J. Rock Mech. Min. Sci., 41(8), 1329–1364.
Randles, P. W., and Libersky, L. D. (1996). “Smoothed particle hydrodynamics: Some recent improvements and applications.” Comput. Methods Appl. Mech. Eng., 139(1–4), 375–408.
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.
Schreyer, H. L., Sulsky, D. L., and Zhou, S.-J. (2002). “Modeling delamination as a strong discontinuity with the material point method.” Comput. Methods Appl. Mech. Eng., 191(23–24), 2483–2507.
Shi, G.-H. (1991). “Manifold method of material analysis.” Transactions of the 9th Army Conf. on Applied Mathematics and Computing, U.S. Army Research Office, Minneapolis, 57–76.
Shi, G.-H., and Goodman, R. E. (1989). “Generalization of two-dimensional discontinuous deformation analysis for forward modelling.” Int. J. Numer. Anal. Methods Geomech., 13(4), 359–380.
Strouboulis, T., Babuška, I., and Copps, K. (2000a). “The design and analysis of the generalized finite element method.” Comput. Methods Appl. Mech. Eng., 181(1–3), 43–69.
Strouboulis, T., Copps, K., and Babuška, I. (2000b). “The generalized finite element method: An example of its implementation and illustration of its performance.” Int. J. Numer. Methods Eng., 47(8), 1401–1417.
Sulsky, D., Chen, Z., and Schreyer, H. L. (1994). “A particle method for history-dependent materials.” Comp. Methods Appl. Mech. Eng., 118(1–2), 179–196.
Sulsky, D., Zhou, S.-J., and Schreyer, H. L. (1995). “Application of a particle-in-cell method to solid mechanics.” Comput. Phys. Commun., 87(1–2), 236–252.
Tang, C. A., Lin, P., Wong, R. H. C., and Chau, K. T. (2001). “Analysis of crack coalescence in rock-like materials containing three flaws—Part II: Numerical approach.” Int. J. Rock Mech. Min. Sci., 38(7), 925–939.
Tsay, R.-J., Chiou, Y.-J., and Chuang, W.-L. (1999). “Crack growth prediction by manifold method.” J. Eng. Mech., 125(8), 884–890.
Van Vliet, M. R.-A. (2000). “Size effect in tensile fracture of concrete and rock.” Ph.D. thesis, Faculty of Civil Engineering, Delft Univ. of Technology, Delft, the Netherlands.
Weibull, W. (1939). “A statistical theory of the strength of materials.” Ing. Vet. Ak. Handl., 151, 5–44.
Wong, L. N. Y., and Einstein, H. H. (2009a). “Crack coalescence in molded gypsum and Carrara marble: Part 1. Macroscopic observations and interpretation.” Rock Mech. Rock Eng., 42(3), 475–511.
Wong, L. N. Y., and Einstein, H. H. (2009b). “Crack coalescence in molded gypsum and Carrara marble: Part 2—Microscopic observations and interpretation.” Rock Mech. Rock Eng., 42(3), 513–545.
Wong, L. N. Y., and Einstein, H. H. (2009c). “Systematic evaluation of cracking behavior in specimens containing single flaws under uniaxial compression.” Int. J. Rock Mech. Min. Sci., 46(2), 239–249.
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.
Wu, Z., and Wong, L. N. Y. (2012). “Frictional crack initiation and propagation analysis using the numerical manifold method.” Comput. Geotech., 39, 38–53.
Yang, S. Q., Yang, D. S., Jing, H. W., Li, Y. H., and Wang, S. Y. (2012). “An experimental study of the fracture coalescence behaviour of brittle sandstone specimens containing three fissures.” Rock Mech. Rock Eng., 45(4), 563–582.
York, A. R., Sulsky, D., and Schreyer, H. L. (2000). “Fluid-membrane interaction based on the material point method.” Int. J. Numer. Methods Eng., 48(6), 901–924.
Yu, M.-H., Zan, Y.-W., Zhao, J., and Yoshimine, M. (2002). “A unified strength criterion for rock material.” Int. J. Rock Mech. Min. Sci., 39(8), 975–989.
Zhou, X. P., Bi, J., and Qian, Q. H. (2015). “Numerical simulation of crack growth and coalescence in rock-like materials containing multiple pre-existing flaws.” Rock Mech. Rock Eng., 48(3), 1097–1114.
Zhou, X. P., Cheng, H., and Feng, Y. F. (2014). “An experimental study of crack coalescence behaviour in rock-like materials containing multiple flaws under uniaxial compression.” Rock Mech. Rock Eng., 47(6), 1961–1986.
Information & Authors
Information
Published In
International Journal of Geomechanics
Volume 16 • Issue 4 • August 2016
Copyright
© 2016 American Society of Civil Engineers.
History
Received: Oct 21, 2014
Accepted: Jun 24, 2015
Published online: Jan 8, 2016
Discussion open until: Jun 8, 2016
Published in print: Aug 1, 2016
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.