Failure Process of Brittle Rock Using Smoothed Particle Hydrodynamics
Publication: Journal of Engineering Mechanics
Volume 139, Issue 11
Abstract
This paper presents a numerical procedure based on smoothed particle hydrodynamics (SPH) to analyze the failure process of a rock medium by predicting the initiation of microcracks. The subsequent propagation of cracks has also been analyzed without any special treatment or assumption regarding fracturing process. The procedure for implementing softening elastoplastic model has been discussed in the SPH framework. For failure of a rock specimen under uniaxial compression, the Drucker-Prager yield criterion is used in the elastic-plastic constitutive model by considering associative and nonassociative plastic flow rules. The Rankine maximum tensile failure criterion is implemented to model the tensile failure of a circular rock specimen. The results obtained from this study have been compared with laboratory tests and existing analytical solutions. It is found that the developed procedure has the potential to provide useful information to understand the key physical phenomena that occur in the failure process.
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References
Benz, W., and Asphaug, E. (1995). “Simulations of brittle solids using smooth particle hydrodynamics.” Comput. Phys. Commun., 87(1-2), 253–265.
Benz, W., Cameron, A., and Melosh, H. (1989). “The origin of the moon and the single-impact hypothesis III.” Icarus, 81(1), 113–131.
Blair, S., and Cook, N. (1998). “Analysis of compressive fracture in rock using statistical techniques: Part I. A non-linear rule-based model.” Int. J. Rock Mech. Min. Sci., 35(7), 837–848.
Brady, B. (1970). “A mechanical equation of state for brittle rock part ı–the pre-failure behavior of brittle rock.” Int. J. Rock Mech. Min. Sci. Geomech. Abstr., 7(4), 385–421.
Bui, H., Fukagawa, R., Sako, K., and Ohno, S. (2008). “Lagrangian meshfree particles method (SPH) for large deformation and failure flows of geomaterial using elastic–plastic soil constitutive model.” Int. J. Numer. Anal. Methods Geomech., 32(12), 1537–1570.
Chen, S., Yue, Z., and Tham, L. (2004). “Digital image-based numerical modeling method for prediction of inhomogeneous rock failure.” Int. J. Rock Mech. Min. Sci., 41(6), 939–957.
Cleary, P., and Das, R. (2008). “The potential for SPH modelling of solid deformation and fracture.” Proc., IUTAM Symp. on Theoretical, Computational and Modelling Aspects of Inelastic Media, Springer, Dordrecht, Netherlands, 287–296.
Cleary, P., and Monaghan, J. (1999). “Conduction modelling using smoothed particle hydrodynamics.” J. Comput. Phys., 148(1), 227–264.
Cleary, P. and Prakash, M. (2004). “Discrete-element modelling and smoothed particle hydrodynamics: Potential in the environmental sciences.” Philos. Trans. R. Soc. London, Ser. A, 362(1822), 2003–2030.
Colmenares, L., and Zoback, M. (2002). “A statistical evaluation of intact rock failure criteria constrained by polyaxial test data for five different rocks.” Int. J. Rock Mech. Min. Sci., 39(6), 695–729.
de Souza Neto, E., Neto, E., Periæ, D., and Owen, D. (2008). Computational methods for plasticity: Theory and applications, Wiley, Chichester, U.K.
Fang, Z., and Harrison, J. (2002). “Development of a local degradation approach to the modelling of brittle fracture in heterogeneous rocks.” Int. J. Rock Mech. Min. Sci., 39(4), 443–457.
Gingold, R., and Monaghan, J. (1977). “Smoothed particle hydrodynamics-theory and application to non-spherical stars.” Mon. Not. R. Astron. Soc., 181, 375–389.
Gray, J., Monaghan, J., and Swift, R. (2001). “SPH elastic dynamics.” Comput. Methods Appl. Mech. Eng., 190(49-50), 6641–6662.
Homand-Etienne, F., Hoxha, D., and Shao, J. (1998). “A continuum damage constitutive law for brittle rocks.” Comput. Geotech., 22(2), 135–151.
Hondros, G. (1959). “The evaluation of Poisson’s ratio and the modulus of materials of a low tensile resistance by the Brazilian (indirect tensile) test with particular reference to concrete.” Aust. J. Appl. Sci., 10(3), 243–268.
Li, L., Lee, P., Tsui, Y., Tham, L., and Tang, C. (2003). “Failure process of granite.” Int. J. Geomech., 3(1), 84–98.
Libersky, L., Petschek, A., Carney, T., Hipp, J., and Allahdadi, F. (1993). “High strain Lagrangian hydrodynamics: A three-dimensional SPH code for dynamic material response.” J. Comput. Phys., 109(1), 67–75.
Monaghan, J. (1992). “Smoothed particle hydrodynamics.” Annu. Rev. Astron. Astrophys., 30, 543–574.
Monaghan, J. (1994). “Simulating free surface flows with SPH.” J. Comput. Phys., 110(2), 399–406.
Monaghan, J., and Kocharyan, A. (1995). “SPH simulation of multi-phase flow.” Comput. Phys. Commun., 87(1–2), 225–235.
Morris, J., Fox, P., and Zhu, Y. (1997). “Modeling low Reynolds number incompressible flows using SPH.” J. Comput. Phys., 136(1), 214–226.
Morris, J., and Monaghan, J. (1997). “A switch to reduce SPH viscosity.” J. Comput. Phys., 136(1), 41–50.
Nasseri, M., Grasselli, G., and Mohanty, B. (2010). “Fracture toughness and fracture roughness in anisotropic granitic rocks.” Rock Mech. Rock Eng., 43(4), 403–415.
Ortiz, M., Leroy, Y., and Needleman, A. (1987). “A finite element method for localized failure analysis.” Comput. Methods Appl. Mech. Eng., 61(2), 189–214.
Paterson, M., and Wong, T. (2005). Experimental rock deformation: The brittle field, 2nd Ed., Springer, Berlin.
Potyondy, D., and Cundall, P. (2004). “A bonded-particle model for rock.” Int. J. Rock Mech. Min. Sci., 41(8), 1329–1364.
Randles, P., and Libersky, L. (1996). “Smoothed particle hydrodynamics: Some recent improvements and applications.” Comput. Methods Appl. Mech. Eng., 139(1–4), 375–408.
Regueiro, R. (2010). “On finite strain micromorphic elastoplasticity.” Int. J. Solids Struct., 47(6), 786–800.
Scholz, C. (1968). “Microfracturing and the inelastic deformation of rock in compression.” J. Geophys. Res., 73(4), 1417–1432.
Shockey, D., Curran, D., Seaman, L., and Rosenberg, J. (1974). “Fragmentation of rock under dynamic loads.” Int. J. Rock Mech. Min. Sci. Geomech. Abstr., 11(8), 303–317.
Sprunt, E., and Brace, W. (1974). “Direct observation of microcavities in crystalline rocks.” Int. J. Rock Mech. Min. Sci. Geomech. Abstr., 11(4), 139–150.
Steif, P. (1984). “Crack extension under compressive loading.” Eng. Fract. Mech., 20(3), 463–473.
Swegle, J., Hicks, D., and Attaway, S. (1995). “Smoothed particle hydrodynamics stability analysis.” J. Comput. Phys., 116(1), 123–134.
Tang, C., Liu, H., Lee, P., Tsui, Y., and Tham, L. (2000). “Numerical studies of the influence of microstructure on rock failure in uniaxial compression—part. I: Effect of heterogeneity.” Int. J. Rock Mech. Min. Sci., 37(4), 555–569.
Wang, Y., and Tonon, F. (2010). “Calibration of a discrete element model for intact rock up to its peak strength.” Int. J. Numer. Analyt. Meth. Geomech., 34(5), 447–469.
Wawersik, W., and Brace, W. (1971). “Post-failure behavior of a granite and diabase.” Rock Mech. Rock Eng., 3(2), 61–85.
Wawersik, W., and Fairhurst, C. (1970). “A study of brittle rock fracture in laboratory compression experiments.” Int. J. Rock Mech. Min. Sci. Geomech. Abstr., 7(5), 561–564.
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Published In
Journal of Engineering Mechanics
Volume 139 • Issue 11 • November 2013
Pages: 1551 - 1565
Copyright
© 2013 American Society of Civil Engineers.
History
Received: Jun 1, 2012
Accepted: Jan 9, 2013
Published online: Jan 11, 2013
Published in print: Nov 1, 2013
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