[en] polyaxial; [en] intermediate principal stress; [en] octahedral sections; [en] meridian sections; [en] limestone; [en] rock; [en] yield surface
Abstract :
[en] The present study investigates the influences of the confining pressure and the intermediate principal stress on the mechanical behaviour of a porous limestone. True triaxial tests are carried out on a broad range of confining stresses covering both brittle and ductile regimes. The experiments included the special cases of triaxial compression, extension and isotropic compression, as well as tests at constant levels of the intermediate principal stress. The resulting stress-strain curves and yield stresses are then discussed. Three-dimensional yield envelopes are subsequently built in meridian and octahedral planes. The shape of the octahedral sections changes with the mean stress from triangular to hexagonal and then quasi circular. At even higher mean stresses, the evolution continues towards a triangle with apexes oriented in the direction of triaxial extension stress states. Various existing yield criteria are fitted and compared to the experimental data. Finally, a three-dimensional yield surface is proposed combining the previous observations.
Charlez P Rock mechanics. Pet Appl Paris: Technip 1997.
Papamichos E Constitutive laws for geomaterials. Oil Gas Sci Technol-Rev IFP 1999, 54:759-771.
Fjaer E, Holt RM, Horsud P, Raaen AM, Risnes R Petroleum related rock mechanics 2008, Elsevier, Amsterdam.
Shah KR An elastoplastic constitutive model for brittle-ductile transition in porous rocks. Int J Rock Mech Min Sci 1997, 34(283):e1-e13.
Wong TF, David C, Zhu W The transition from brittle faulting and cataclastic flow in porous sandstones: mechanical deformation. J Geophys Res 1997, 102:3009-3025.
Wong TF, Baud P Mechanical compaction of porous sandstone. Oil & Gas Sci Technol-Rev IFP 1999, 54:715-727.
Bésuelle P, Desrues J, Raynaud S Experimental characterization of the localisation phenomenon of a Vosges sandstone in a triaxial cell. Int J Rock Mech Min Sci 2000, 37:1223-1237.
Papamichos E, Tronvoll J, Vardoulakis I, Labuz JF, Skjaerstein A, Unander TE, Sulem J., et al. Constitutive testing of Red Wildmoor sandstone. Mech Cohesive Frict Maters 2000, 5:1-40.
Klein E, Baud P, Reuschlé T, Wong TF Mechanical behaviour and failure mode of Bentheim sandstone under triaxial compression. Phys Chem Earth (A) 2001, 26:21-25.
Tembe S, Vajdova V, Baud P, Zhu W, Wong TF A new methodology to delineate the compactive yield cap of two porous sandstones under undrained condition. Mech Maters 2007, 39:513-523.
Elliott GM, Brown ET Yield of a soft, high porosity rock. Géotechnique 1985, 35:413-423.
Shao JF, Henry JP Development of an elastoplastic model for porous rocks. Int J Plast 1991, 7:1-13.
Papamichos E, Brignoli M, Santarelli FJ An experimental and theoretical study of a partially saturated collapsible rock. Mech Cohesive Frict Maters 1997, 2:251-278.
Vincké O, Boutéca MJ, Piau JM, Fourmaintraux D Study of the effective stress at failure. In: Proceedings biot conference on poromechanics. Louvain-La-Neuve, Belgique; 14-16 September 1998. p. 635-9.
Shao JF, Homand S Comportement plastique des roches poreuses. Elastoplasticité des sols et des Roches 2002, 203-220. Lavoisier, Paris. P.Y. Hicher, J.F. Shao (Eds.).
Vajdova V, Baud P, Wong TF Compaction, dilatancy, and failure in porous carbonate rocks. J Geophys Res 2004, B05204.
Xie SY, Shao JF Elastoplastic deformation of a porous rock and water interaction. Int J Plast 2006, 22. 2195-25.
Fortin J, Stanchits S, Dresen G, Guégen Y Micro-mechanisms involved during inelastic deformation of porous carbonate rocks. In: Proceedings of the fourth biot conference on poromechanics. New York; 8-10 June 2009. p. 378-83.
Schroeder C Du coccolithe au réservoir pétrolier. Approche phénoménologique du comportement mécanique de la craie en vue de sa modélisation à différentes échelles. PhD thesis. University of Liège, Liège, Belgium; 2002.
Baud P, Schubnel A, Wong TF Dilatancy, compaction, and failure mode in Solnhofen limestone. J Geophys Res 2000, 105:19289-19303.
Wong TF, David C, Menéndez B Mechanical compaction. Mechanics of fluid-saturated rocks 2004, 55-114. Academic Press, New York. M. Boutéca, Y. Guéguen (Eds.).
Song I, Haimson B Polyaxial strength criteria and their use in estimating in situ stress magnitudes from borehole breakout dimensions. Int J. Rock Mech Min Sci 1997, 35:3-4.
Takahashi M, Koide H Effect of the intermediate principal stress on strength and deformation behaviour at depths shallower than 2000m. In: Proceeding of the international symposium rock at great depth. Pau; 28-31 August 1989. p. 19-26.
Cai M Influence of the intermediate principal stress on rock fracturing and strength near excavation boundaries-insight from numerical modelling. Int J Rock Mech Min Sci 2008, 45:763-772.
Haimson B, Chang C A new true triaxial cell for testing mechanical properties of rock, and its use to determine rock strength and deformability of Westerly granite. Int J Rock Mech Min Sci 2000, 37:285-296.
Wu W, Kolymbas D On some issues in triaxial extension tests. Geotech Test J 1991, 14:276-287.
Hickman RJ Formulation and implementation of a constitutive model for soft rock. PhD thesis. Virginia Polytechnic Institute and State University, Blacksburg, Virginia; 2004.
Dehler W, Labuz JF Stress path testing of an anisotropic sandstone. J Geotech Geoenviron Eng 2007, 133:116-119.
Hobbs DW The strength of coal under biaxial compression. Colliery Eng 1962, 39:285-290.
Yun X, Mitri HS, Yang X, Wang Y Experimental investigation into the biaxial strength of granite. Int J Rock Mech Min Sci 2010, 47:334-341.
Mogi K Effect of the intermediate principal stress of failure. J Geophys Res 1967, 72:5117-5131.
Mogi K Fracture and flow of rocks under high triaxial compression. J Geophys Res 1971, 76:1255-1269.
Ko HY, Scott RF Deformation of sand in shear. J Soil Mech Found Div 1967, 93:283-310.
Michelis P A true triaxial cell for low and high confining pressure experiments. Int J Rock Mech Min Sci 1985, 22:183-188.
Tshibangu JP Etude des effets du confinement sur le comportement mécanique des roches pour application au calcul des ouvrages souterrains. PhD thesis. Faculté Polytechnique de Mons, Mons, Belgium; 1993.
Alexeev AD, Revva VN, Alyshev NA, Zhitlyonok DM True triaxial loading apparatus and its application to coal outburst prediction. Int J Coal Geology 2004, 58:245-250.
Sture S, Desai CS Fluid cushion truly triaxial or multiaxial testing device. Geotech Test J 1979, 2:20-33.
Hegemier GA, Read HE On deformation and failure of brittle solids: some outstanding issues. Mech of Mater 1985, 4:215-259.
Duchĉne P Comportement géomécanique d'un limon sec. PhD thesis. Faculté Universitaire des Sciences Agronomiques de Gembloux, Gembloux, Belgium; 1997.
Alsayed MI Utilising the Hoek triaxial cell for multiaxial testing of hollow rock cylinders. Int J Rock Mech Min Sci 2002, 39:355-366.
Lee DH, Juang CS, Lin HM, Yeh SH Mechanical behaviour of Tien-Lao mudstone in hollow cylinder tests. Can Geotech J 2002, 39:744-756.
Smart BGD, Sommerville JM, Crawford BR A rock test cell with true triaxial capability. Geol Geotech Eng 2000, 17:157-176.
Jaeger JC, Hoskins ER Rock failure under the confined brazilian test. J Geophys Res 1966, 71:2651-2659.
Tshibangu JP The effect of polyaxial confining state on the behaviour of two limestones. In: Proceedings environmental a nd safety concerns in underground construction. New York; 29 June-2 July 1997. p. 465-70.
Colmenares L, Zoback MD A statistical evaluation of intact rock failure criteria constrained by polyaxial test data for five different rocks. Int J Rock Mech Min Sci 2002, 39:695-729.
Haimson B True triaxial stresses and the brittle fracture of rock. Pure Appl Geophys 2006, 163:1101-1130.
Chang C, Haimson B Non-dilatant deformation and failure mechanism in two long valley Caldera rocks under true triaxial compression. Int J Rock Mech Min Sci 2005, 42:402-414.
Paterson MS, Wong TF Experimental rock deformation-the brittle field 2005, Springer, Berlin.
Michelis P Polyaxial yielding of granular rock. J Eng Mech 1985, 111:1049-1066.
Nayak GC, Zienkiewicz OC Convenient form of stress invariants for plasticity. J Struct Div 1972, 98:949-954.
Yu MH, Zan YW, Zhao J, Yoshimine M A unified strength criterion for rock materials. Int J Rock Mech Min Sci 2002, 39:975-989.
Jaeger JC, Cook NGW, Zimmerman RW Fundamentals of rock mechanics 2007, Wiley-Blackwell, Oxford.
Desai CD, Salami MR A constitutive model and associated testing for soft rock. Int J Rock Mech Min Sci 1987, 24:299-307.
Kim MK, Lade PV Modelling rock strength in three dimensions. Int J Rock Mech Min Sci 1984, 21:21-33.
Descamps F, Tshibangu JP Modelling the limiting envelopes of rocks in the octahedral plane. Oil Gas Sci Technol-Rev IFP 2007, 62:683-694.
Descamps F Etude du comportement des roches poreuses saturées aux conditions de grande profondeur. PhD thesis. Faculté Polytechnique de Mons, Mons, Belgium; 2007.
Willam KJ, Warnke EP Constitutive model for the triaxial behaviour of concrete. In: Proceedings IABSE seminar on "Concrete structures subjected to triaxial stresses" ISMES. Bergamo; 17-18 May 1974. 30 p.
Chen WF, Han DJ Plasticity for structural engineers. Fort Lauderdale: J Ross Pub 2007.
Lade PV Elasto-plastic stress-strain theory for cohesionless soil with curved yield surfaces. Int J Solids Struct 1977, 13:1014-1035.
Bigoni D, Piccolroaz A Yield criteria for quasibrittle and frictional materials. Int J Solid Struct 2004, 41:2855-2878.
Zhu W, Montesi LGJ, Wong TF Shear-enhanced compaction and permeability reduction: triaxial extension tests on porous sandstones. Mech Mater 1997, 25:199-214.
Yu MH Advances in strength theories for materials under complex stress state in the 20th century. Appl Mech Rev 2002, 55:169-218.
Mestat P Modélisation élastoplastique des sols-I. Chargements monotones. Elastoplasticité des sols et des roches 2002, 91-157. Lavoisier, Paris. P.Y. Hicher, J.F. Shao (Eds.).
Drucker DC, Prager W Soil mechanics and plastic analysis for limit design. Q Appl Math 1952, 10:157-165.
Wiebols GA, Cook NGW An energy criterion for the strength of rock in polyaxial compression. Int J Rock Mech Min Sci 1968, 5:529-549.
Hoek E, Carranza-Torres C, Corkuml B Hoek-Brown criterion-2002 edition. In: Proceedings NARMS-TAC conference. Toronto; 7-10 July 2002. p. 267-73.
Al-Ajmi AM, Zimmerman RW Relation between the Mogi and the Coulomb failure criteria. Int J Rock Mech Min Sci 2005, 42:431-439.
Benz T, Schwab R, Kauther RA, Vermeer PAA Hoek-Brown criterion with intrinsic material strength factorization. Int J Rock Mech Min Sci 2008, 45:210-222.
Zhang L, Zhu H Three-dimensional Hoek-Brown strength criterion for rocks. J Geotech Geoenviron Eng 2009, 133:1128-1135.
Bardet JP Lode dependences for isotropic pressure-sensitive elastoplastic materials. Trans ASME 1990, 57:498-506.
Maiolino S Fonction de charge générale en géomécanique: application aux travaux souterrains. PhD thesis. Ecole Polytechnique, Palaiseau, France; 2006.
Di Maggio FL, Sandler IS Material model for granular soils. J Eng Mech 1971, 97:935-970.
Khan AS, Xiang Y, Huang S Behavior of Berea sandstone under confining pressure, Part I: Yield and failure surfaces, and nonlinear elastic response. Int J Plast 1991, 7:607-624.
Roscoe KH, Burland JB On the generalized behaviour of 'wet' clay. Engineering plasticity 1968, 535-609. Cambridge University Press, Cambridge. J. Heyman, F.A. Leckie (Eds.).
Peric D, Ayari MA Influence of Lode's angle on the pore pressure generation of soils. Int J Plast 2002, 18:1039-1059.
Desai CS, Somasundaram S, Frantziskonis G A hierarchical approach for constitutive modelling of geologic materials. Int J Numer Anal Methods Geomech 1986, 10:225-257.
Lagioia R, Puzrin AM, Potts DM A new versatile expression for yield and plastic potential surfaces. Comput Geotech 1996, 19:171-191.
Aubertin M, Li L A porosity dependant inelastic criterion for engineering materials. Int J Plast 2004, 20:2179-2208.
Mortara G A new yield and failure criterion for geomaterials. Géotechnique 2008, 58:125-132.
Ramos da Silva M, Schroeder C, Verbrugge JC Poroelastic behaviour of a water-saturated limestone. Int J Rock Mech Min Sci 2010, 47:797-807.
Baxevanis T, Papamichos E, Flornes O, Larsen I Compaction bands and induced permeability reduction in Tufeau de Maastricht calcarenite. Acta Geotech 2006, 1:123-135.
Hoek E The strength of jointed rock masses. Géotechnique 1983, 23:187-223.