Abstract
Some new results in rock mechanics and some applications are presented. First, it is shown how an elastic/viscoplastic nonassociated constitutive equation can be derived for rock-like and particulate materials. This constitutive equation is based on the fundamental concept of compressibility/dilatancy. Damage and microcracking energy are discussed. Examples are given to demonstrate that it is possible to predict where the rock near underground openings is dilatable and where is compressible, where and when short-term or long-term failure is to be expected, the amount of rock involved in evolutive damage, etc.
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REFERENCES
Ali I. Abdel-Hadi, N. D. Cristescu, O. Cazacu, and Ray A. Bucklin, “Development of a new technique for measuring volume change of dry particulate systems under very low confining pressures,” in: Proc. 2000 ASME Int. Mech. Eng.Congr. and Expos. on Recent Trends in Constitutive Modeling of Advanced Materials, November 5-10, Orlando, Florida AMD, 239 (2000), pp. 65–77.
Ali I. Abdel-Hadi and N. D. Cristescu, “Testing and modeling of dry cohesive particulate materials,” in: Proc. Summer Conf. on Mechanics of Materials (June 27-29, 2001), Univ. of California, San Diego (2001) (in print).
I. V. Baklashov and V. A. Kartozia, Mechanics of Rocks [in Russian], Nedra, Moscow (1975).
Z. T. Bieniawski, “Mechanism of brittle fracture of rock, Part I-Theory of the fracture process, Part II-Experimental studies, and Part III - Fracture in tension and under long-term loading,” Int. J. Rock Mech. Min. Sci., No. 4, 365–430 (1967).
Z. T. Bieniawski, Rock Mechanics Design in Mining and Tunneling, Balkema, Rotterdam (1984).
W. F. Brace, B. W. Paulding, and C. Scholz, “Dilatancy in the fracture of crystalline rocks,” J. Geophys. Res., 71, No. 16, 3939–3953 (1966).
M. Brignoli and L. Sartori, “Incremental constitutive relations for the study of wellbore failure,” Int. J. Rock Mech. Min.Sci.& Geomech. Abstr., 30, No. 7, 1319–1322 (1993).
O. Cazacu, An Elastic/Viscoplastic Constitutive Equation for an Anisotropic Rock, Ph.D. Thesis, Univ. of Science and Technologies of Lille, France (1995).
O. Cazacu and N. D. Cristescu, “Invariant formulation of an elastic/viscoplastic constitutive equation for anisotropic rock,” in: Proc. 9th Int. Conf. (August, Paris, France), 2 (1999), pp. 869–873.
O. Cazacu and N. D. Cristescu, “A paraboloid failure surface for transversely isotropic materials,” Mech. Mater., 31, 381–393 (1999).
O. Cazacu, J. Jin, and N. D. Cristescu, “A new constitutive model for alumina powder compaction,” KONA, Powder and Particle, 15, 103–112 (1997).
S. Cleja-Tigoiu, “Elasto-viscoplastic constitutive equations for rock-type materials (finite deformation),” Int. J. Engng.Sci., 29, 1531–1544 (1991).
D. F. Coates, Rock Mechanics Principles, CANMET, Canada (1981).
N. D. Cristescu, “Rock plasticity,” in: A. Sawczuk and G. Bianchi (eds.), Plasticity Today: Modelling, Methods and Applications, Elsevier Applied Sic. Publ. (1985), pp. 643–655.
N. D. Cristescu, “Viscoplastic creep of rocks around horizontal tunnels,” Int. J. Rock Mech. Min. Sci.& Geomech. Abstr., 22, No. 6, 453–459 (1985).
N. D. Cristescu, “Damage and failure of viscoplastic rock-like materials,” Int. J. Plasticity, 2, No. 2, 189–204 (1986).
N. D. Cristescu, D. Fota, and E. Medves, “Tunnel support analysis incorporating rock creep,” Int. J. Rock Mech. Min.Sci., 24, No. 6, 321–330 (1987).
N. D. Cristescu and E. Medves, “Wood compressibility in mining applications,” in: Actes Bordeaux (1988), pp. 461–470.
N. D. Cristescu, Rock Rheology, Kluwer Academic, Dordrecht (1989).
N. D. Cristescu and I. Duda, “A tunnel support analysis incorporating rock creep and the compressibility of a broken rock stratum,” Comput. Geotechn., 7, No. 3, 239–254 (1989).
N. D. Cristescu, “Nonassociated elastic/viscoplastic constitutive equations for sand,” Int. J. Plasticity, 7, 41–64 (1991).
N. D. Cristescu, “Constitutive equation for rock salt and mining applications,” in: Proc. 7th Int. Symp. on Salt, Elsevier Science Publ., Amsterdam (1992), pp. 105–115.
N. D. Cristescu, “A general constitutive equation for transient and stationary creep of rock salt,” Int. J. Rock Mech. Min.Sci. &; Geomech. Abstr., 30, No. 2, 125–140 (1993).
N. D. Cristescu, “Failure and creep failure around an underground opening,” in: A. G. Pasamesmetoglu, T. Kawamoto, B. N. Whittaker, and O. Aydan (eds.), Assessment and Prevention of Failure Phenomena in Rock Engineering, Balkema, Rotterdam (1993), pp. 205–210.
N. D. Cristescu, “Rock rheology,” in: J. A. Hudson (editor in chief), Comprehensive Rock Engineering, Vol. 1, Rock Mechanics Principles, Pergamon Press (1993), pp. 523–544.
N. D. Cristescu and U. Hunsche, “A comprehensive constitutive equation for rock salt: determination and application,” in: Proc. 3rd Conf. on the Mechanical Behavior of Salt (September 14, Paris), 16 (1993), p. 15.
N. D. Cristescu, “Viscoplasticity of geomaterials,” in: N. D. Cristescu and G. Gioda (eds.), Visco-Plastic Behaviour of Geomaterials, Springer-Verlag, Vienna-New York (1994), pp. 103–207.
N. D. Cristescu, “A procedure to determine nonassociated constitutive equations for geomaterials,” Int. J. Plasticity, 10, No. 2, 103–131 (1994).
N. D. Cristescu, “Time effect in rock surrounding a horizontal tunnel,” in: P. L. Nelson and S. E. Laubach (eds.), Proc. 1st NARMS Symp., Balkema, Rotterdam (1994), pp. 657–664.
N. D. Cristescu, I. R. Ionescu, and I. Rosca, “Short communication on a numerical analysis of the foot-floor interaction in long wall workings,” Int. J. Numer. Analyt. Meth. Geomech., 18, 641–652 (1994).
N. D. Cristescu, “Failure of compressible/dilatant geomaterials,” ASME, Reprint No. AMR146, 102–106 (1994).
N. D. Cristescu and I. Paraschiv, “On the optimal shape of rectangular-like caverns,” Int. J. Rock Mech. Min. Sci., 32, No. 4, 285–300 (1995).
N. D. Cristescu and O. Cazacu, “Viscoplasticity of anisotropic rock,” in: S. Tanimura and A. S. Khan (eds.), Proc. 5th Int. Symp. on Plasticity and Its Current Applications, Gordon and Breach (1995), pp. 499–502.
N. D. Cristescu, “Evolutive damage in rock salt,” in: Proc. 4th Conf. on the Mechanical Behavior of Salt, Trans. Tech.Publ., Clausthal-Zellerfeld (1996), pp. 131–141.
N. D. Cristescu, “Stability of large underground caverns in rock salt,” in: Rock Mechanics, Balkema, Rotterdam (1996), pp. 101–107.
N. D. Cristescu and I. Paraschiv, “Creep, damage and failure around large rectangular-like caverns and galleries,” Mech.Cohes.-Frict. Mater., No. 1, 1–33 (1996).
N. D. Cristescu, “Design of yieldable tunnel supports for creeping rocks,” in: Trans. of the Society for Mining, Metallurgy, and Exploration, 300 (1997), pp. 1847–1854.
N. D. Cristescu and U. Hunsche, Time Effects in Rock Mechanics, John Wiley &; Sons, Chichester-New York-Weinheim-Brisbane-Singapore-Toronto (1998).
N. D. Cristescu, “Theoretical approach to sand liquefaction,” in: Proc. Geo-Denver. Soil Dynamics and Liquefaction (2000), pp. 1–9.
N. D. Cristescu and O. Cazacu, “Viscoplasticity of geomaterials,” in: M. Zaman, G. Gioda, and J. Booker (eds.), Modeling in Geomechanics, John Wiley &; Sons (2000), pp. 129–153.
A. Dahou, J. F. Shao, and M. Bederiat, “Experimental and numerical investigations on transient creep of porous chalk,” Mech. Mater., 21, 147–158 (1995).
A. M. Galperin and E. M. Shafarenko, Rheological Computation of Structures in Rocks [in Russian], Nedra, Moscow (1977).
U. Glabisch, Stoffmodell fur Grenzzustande im Salzgestein zur Berechnung von Gebirgshohlraumen, Ph.D. Dissertation, Technical University “Carolo, Wilhelmina,” Braunschweig, Germany (1997).
M. N. Goldstein, Mechanical Properties of Soils [in Russian], Stroiizdat, Moscow (1971).
R. E. Goodman, Introduction to Rock Mechanics, John Wiley, New York (1980).
S. S. Grigorian and V. A. Ioselevich, “Mechanics of soils,” in: Mechanics in the SSSR after 50 Years [in Russian], Vol. 3, Nauka, Moscow (1972).
A. Hettler, G. Gudehus, and I. Vardoulakis, “Stress-strain behaviour of sand in triaxial tests,” in: G. Gudehus, F. Darve, and L. Vardoulakis (eds.), Results of the Int. Workshop on Constitutive Relations for Soils, Balkema, Rotterdam (1984), pp. 55–66.
E. Hoek and E. T. Brown, Underground Excavations in Rock, The Institution of Mining and Metallurgy, London (1980).
J. A. Hudson (editor-in-chief), Comprehensive Rock Engineering: Principles, Practices &; Projects, Pergamon Press, Oxford-New York-Seoul-Tokyo (1993).
U. Hunsche, Private Communications (1988).
I. R. Ionescu and M. Sofonea, Functional and Numerical Methods in Viscoplasticity, Oxford Sci. Publ. (1993).
J. C. Jaeger and N. G. W. Cook, Fundamentals of Rock Mechanics, Chapman and Hall, London (1979).
J. Jin and N. D. Cristescu, “A constitutive model for powder materials,” Trans. ASME, J. Eng. Mater. Technol., 120, No. 2, 97–104 (1998).
J. Jin and N. D. Cristescu, “An elastic/viscoplastic model for transient creep of rock salt,” Int. J. Plasticity, 14, No. 1-3, 85–107 (1998).
A. R. Jumikis, Rock Mechanics, Trans. Tech. Publ., Clausthal-Zellerfeld (1983).
Th. von Karman, “Festigkeitsversuche under allseitigen Druck, “ Zeitschrift. Ver. Deutsch. Ing., 55, 1749–1757 (1911).
R. L. Kranz, “The effects of confining pressure and stress difference on static fatigue of granite,” J. Geophys. Research, 85, No. B4, 1854–1866 (1980).
R. L. Kranz, W. J. Harris, and L. C. Neville, “Static fatigue of granite at 200 °C,” Geophys. Research Letters, 9, No. 1, 1–4 (1982).
E. Z. Lajtai and R. H. Schmidtke, “Delayed failure in rock loaded in uniaxial compression,” Rock Mech. Rock Eng., 19, 11–25 (1986).
A. Matei and N. D. Cristescu, “Variation in time of the elastic parameters of rock salt,” in: Proc. Int. Congr. on Rock Mechanics, 2 (1999), pp. 635–639.
A. Matei and N. D. Cristescu, “The effect of volumetric strain on elastic parameters for rock salt,” Mech. Cohes.-Frict.Mater., 5, 113–124 (2000).
A. Nadai, Theory of Flow and Fracture in Solids, Vol. 1, McGraw-Hill, New York (1950).
A. Nadai, Theory of Flow and Fracture of Solid, Vol. 2, McGraw-Hill, New York (1963).
P. A. Nawrocki, M. B. Dusseault, N. D. Cristescu, and R. K. Bratli, “Experimental methods for determining constitutive parameters for nonlinear rock modeling,” in: Yuan (ed.), Computer Methods and Advances in Geomechanics, Balkema, Rotterdam (1997), pp. 831–836.
P. A. Nawrocki, N. D. Cristescu, M. B. Dusseault, and R. K. Bratli, “Experimental methods for determining constitutive parameters for nonlinear rock modeling,” Int. J. Rock Mech. Mining Sci., 36, 659–672 (1999).
L. Obert and W. I. Duvall, Rock Mechanics and the Design of Structures in Rock, John Wiley, New York (1967).
L. Paraschiv-Munteanu and N. D. Cristescu, “Stress relaxation during creep of rocks around deep boreholes,” Int. J. Eng.Sci., 39, 737–754 (2001).
T. Popp, O. Schulze, and H. Kern, Permeation and Development of Dilatancy and Permeability in Rock Salt (2001).
O. Sano, I. Ito, and M. Terada, “Influence of strain rate on dilatancy and strength of Oshima granite under uniaxial compression,” J. Geophys. Research, 86, No. B10, 9299–9311 (1981).
R. H. Schmidtke and E. Z. Lajtai, “The long-term strength of Lac du Bonnet granite,” Int. J. Rock. Mech. Min. Sci. &; Geomech. Abstr., 22, No. 6, 461–465 (1985).
A. Schofield and P. Wroth, Critical State Soil Mechanics, McGraw-Hill, New York (1968).
V. V. Sokolovskii, Statics of Friable Media [in Russian], Gosizdat, Moscow (1954).
D. M. Wood, Soil Behaviour and Critical State Soil Mechanics, Cambridge University Press (1990).
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Cristescu, N.D. New Trends in Rock Mechanics. International Applied Mechanics 38, 1–22 (2002). https://doi.org/10.1023/A:1015364607665
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DOI: https://doi.org/10.1023/A:1015364607665