Abstract
A procedure is proposed and substantiated for automatic tracing the trajectories of the normal tension cracks for a quantitative investigation of their growth and rock deformation under compression. For isolated cracks, the error of hypotheses simplifying models of the processes in question is estimated. For doubly periodic systems of cracks, the features of crack growth and their role in changing the effective properties of medium are considered.
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REFERENCES
A. A. Griffith, “The theory of rupture,” in: Proceedings of the 1st Int. Congress on Applied Mechanics, Delft. (1924).
C. Fairhurst and N. G. W. Cook, “The phenomenon of rock splitting parallel to the direction of maximum compression in the neighbourhood of a surface,” in: Proceedings of the 1st Congress Int. Soc. Rock Mech., 1 (1966).
N. M. Osipenko, “Investigation into mechanism of brittle failure of fractured rocks,” Author's Abstr. Diss. Cand. Techn. Sci., IFZ, Akad. Nauk SSSR, Moscow (1972).
R. V. Gol'dshtein, V. M. Ladygin, and N. M. Osipenko, “Model for brittle failure of slightly porous material under compression and tension,” Fiz.-Tekh. Probl. Razrab. Polezn. Iskop., No. 1 (1974).
I. M. Petukhov, A. M. Lin'kov, V. S. Sidorov, and I. A. Fel'dman, Theory of Protective Seams. Appendix 3: Features of Brittle Failure [in Russian], Nedra, Moscow (1976).
V. N. Odintsev, “Tensile failure of rock mass,” Diss. Dr. Techn. Sci., IPKON, Moscow (1996).
J. P. Berry, “Some kinetic consideration of Griffith criterion for fracture,” J. Mech. Phys. Solids, 8 (1960).
J. B. Walsh, “The effect of cracks on the uniaxial elastic compression of rocks,” J. Geoph. Res., 70 (1965).
J. M. Kemeny and N. G. W. Cook, “Effective moduli, nonlinear deformation, and strength of a cracked elastic solid,” Int. J. Rock Mechanics and Mining Sci. & Geomech. Abstr., 23 (1986).
J. M. Kemeny and N. G. W. Cook, “Micromechanics of deformation in rocks,” in: Toughness Mechanics in Quasi-Brittle Materials, S. P. Shah (ed.), Kluwer Acad. Publ., The Netherlands (1991).
A. N. Stavrogin, “Investigation of limit states and rock deformation,” Izv. Akad. Nauk SSSR, Fiz. Zemli, No. 12 (1969).
P. Tapponier and W. F. Brace, “Development of stress-induced micromechanics in Westerby granite,” Int. J. Rock Mech. Sci. & Geomech. Abstr., 14 (1975).
B. G. Tarasov, “On the statistic nature of deformation in rocks,” Fiz.-Tekh. Probl. Razrab. Polezn. Iskop., No. 6 (1991).
M. V. Kurlenya, V. N. Oparin, and A. A. Eremenko, “Relation of linear block dimensions of rocks to crack opening in the structural hierarchy of masses,” Fiz.-Tekh. Probl. Razrab. Polezn. Iskop., No. 3 (1993).
J. A. L. Napier and A. P. Pierce, “Simulation of extensive fracture formation and interaction in brittle materials,” Mech. of Jointed and Faulted Rock, P. Rossmanith (ed.), Balkema, Rotterdam (1995).
J. A. L. Napier and D. F. Malan, “A visco-plastic discontinuum model of time dependent fracture and seismicity effects in brittle rock,” Int. J. Rock Mechanics and Mining Sci., 34, (1997).
L. N. Germanovich, L. M. Ring, B. J. Carter, A. R. Ingraffea, A. V. Dyskin, and K. B. Ustinov, “Simulation of crack growth and interaction in compression,” in: Proceedings of the 8th Int. Congress on Rock Mech., 1, Balkema, Rotterdam (1995).
A. M. Lin'kov and S. G. Mogilevskaya, “Complex hypersingular integrals and equations in plane elasticity problem,” in: Investigation into Mechanics of Constructions and Materials. Collection of Works [in Russian], LISI, Leningrad (1991).
A. M. Lin'kov and S. G. Mogilevskaya, “Complex hypersingular BEM in plane elasticity problems,” In: Singular Integrals in Boundary-Element Methods, V. Sladek and J. Sladek (eds.), Computational Mechanics Publications, Southampton (1998).
A. M. Lin'kov, Complex Method of Boundary-Integral Equations in the Elasticity Theory [in Russian], Nauka, Saint Petersburg (1999).
A. M. Lin'kov and V. F. Koshelev, “Complex variables BIE and BEM for a plane doubly periodic system of flaws,” J. Chinese Institute of Engineers, 22 (1999).
A. M. Lin'kov, V. V. Zubkov, and M. A. Kheib, “A method of solving three-dimensional problems of seam workings and geological faults,” Fiz.-Tekh. Probl. Razrab. Polezn. Iskop., No. 4 (1997).
L. M. Kachanov, Fundamentals of Fracture Mechanics [in Russian], Nauka, Moscow (1974).
M. P. Savruk, M. P. Osiv, and I. V. Prokopchuk, Numerical Analysis in Plane Problems of Crack Theory [in Russian], Naukova Dumka, Kiev (1989).
F. Erdogan and G. C. Sih, “On the crack extension in plates under plane loading and transverse shear,” Trans. ASME. J. Basic Engineering, 85 (1963).
V. V. Panasyuk and V. V. Berezhnitskii, “Determination of limiting forces under tension of plate with the arc-wise crack,” Vopr. Mekh. Real. Tverd. Tela, No. 3 (1964).
R. V. Gol'dshtein and R. V. Salganik, “Plane problem on curvilinear cracks in elastic body,” Izv. Akad. Nauk SSSR, Mekh. Tverd. Tela, No. 3 (1970).
B. Cotterell and J. R. Rice, “Slightly curved or kinked cracks,” Int. J. Fracture, 16 (1980).
M. P. Savruk, Two-Dimensional Problems of Elasticity Theory for Bodies with Cracks [in Russian], Naukova Dumka, Kiev (1981).
S. G. Mogilevskaya, “Numerical modeling of 2-D smooth crack growth,” Int. J. Fracture, 87 (1997).
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Lin'kov, A.M., Dobroskok, A.A. Numerical Modeling of Rock Deformation under Compression. Journal of Mining Science 37, 371–383 (2001). https://doi.org/10.1023/A:1014268522760
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DOI: https://doi.org/10.1023/A:1014268522760