PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
Tytuł artykułu

Development of a damage model for rock materials under compressive and tensile stress fields

Wybrane pełne teksty z tego czasopisma
Identyfikatory
Warianty tytułu
PL
Opracowanie modelu zniszczeniowego materiałów skalnych pod działaniem pola naprężeń ściskających i rozciągających
Języki publikacji
PL
Abstrakty
PL
Wraz ze wzrostem głębokości i rozmiarów wyrobisk podziemnych, zasięg strefy zniszczenia wokół obiektów podziemnych rośnie, co stanowi poważny problem związany z projektowaniem działań wydobywczych i bezpieczeństwem. Główne przyczyny nieodwracalnych odkształceń to płyniecie plastyczne i proces niszczenia. Większość modeli elasto-plastycznych wykorzystywanych w analizie i projektowaniu obiektów podziemnych uwzględnia jedynie płyniecie plastyczne, a nie pełny proces niszczenia. Dla realistycznego modelowania procesów niszczenia skał należy uwzględnić także inne kluczowe zagadnienia: zmniejszenie sztywności, dylatacje, zmiękczenia, anizotropię skał, znaczne różnice w zachowaniu materiału skalnego pod wpływem obciążeń rozciągających i ściskających. Dlatego też niezbędne są dalsze prace nad modelowaniem procesów niszczenia dla ułatwienia projektowania obiektów podziemnych. W artykule tym przedstawiono krótko aspekty termodynamiczne oraz ogólne rozważania na temat materiałów o malejącej podatności. Następnie podano jasną i dokładną definicję funkcji odporności na zniszczenie wraz z regułami dotyczącymi twardnienia i zmiękczania materiałów. W definicji podatności na zniszczenie wielu autorów uwzględnia jedynie mikro-pęknięcia rozciągające (tryb 1). Ponieważ quasi-kruche materiały, przykładowo skały, ulegają degradacji pod wpływem mikro-spękań spowodowanych przez naprężenia ściskające ora ścinające (tryb 2), wprowadzono odpowiednio dodatnie i ujemne funkcje podatności. Zaproponowano dwa algorytmy do oceny uszkodzeń spowodowanych przez obciążenia rozciągające i ściskające. W końcowej części artykułu zaprezentowano algorytm obliczeniowy opracowanego modelu konstytutywnego.
EN
With increase in depth and size of underground openings, the extent of damage zone around these structures grows and becomes major safety and design issues. The dominant causes of irreversible deformations are plastic flow and damage process. Most of the existing elastic-plastic models employed in the analysis and design of underground structures only consider the plastic flow and not the full damage process. In order to realistically modeling the rock damage process, the important issues such as stiffness degradation, dilatation, softening, anisotropy, and significant differences in rock response under tensile and compressive loadings must be considered. Therefore, developments of realistic damage models are essential in the design process of underground structures. In this paper basic thermodynamic arguments and the general formulation of elastic - degrading material are outline. Then, a more clear and accurate definition of the damage resistance function and its hardening and softening law are established. In the definition of damage yield function, many authors considered only the tensile microcracking (mode 1). Since quasi brittle materials such as rock degrade under compressive and shear microcracking (mode 2), separate positive and negative yield functions are introduced. Accordingly, two different algorithms are proposed to evaluated the damage associated with compressive and tensile loadings. The computational algorithm and the developed constitutive models is presented and the end.
Rocznik
Strony
637--668
Opis fizyczny
Bibliogr. 87 poz., rys., wykr.
Twórcy
autor
  • Department of Mining and Metallurgical Engineering, Amirkabir University of Technology, Teheran, Iran
Bibliografia
  • Alliche A., 2004. Damage model for fatigue loading of concrete. Int. J. Fatigue, 26, 915-921.
  • Basaran C., Nie S., 2004. An irreversible Thermodynamics Theory for Damage Mechanics of Solids. International Journal of Damage Mechanics, 13, 205-223.
  • Badel P., incent Godard V., Leblond J., 2007. Application of some anisotropic damage model to the prediction of the failure of some complex industrial concrete structure. Int. J. Solids and Structures, 44, 5848-5874.
  • Bonora N., Gentile D., Pirondi A., Newaz G., 2005. Ductile damage evolution under triaxial state of stress: theory and experiments. Int. J. Plasticity, 21, 981-1007.
  • Bonora N., Ruggiero A., Esposito L., 2006. CDM modeling of ductile failure in ferritic steels: Assessment of the geometry transferability of model parameters. Int. J. Plasticity, 22, 2015-2047.
  • Boudifa M., Saanouni K., Chaboche J.L., 2009. A micromechanical model for inelastic ductile damage prediction in polycrystalline metals for metal forming. Int. J. Mechanical Sciences, 51, 453-464.
  • Brunig M., 2001. A framework for large strain elastic-plastic damage mechanics based on metric transformation. Int. J. Engrg. Science, 39,1033-1056.
  • Carol I., Rizzi E., Willam K., 1994. A unified theory of elastic degradation and damage based on a loading surface. Int. J. Solids and Structures, 31, 2835-2865.
  • Carol I., Rizzi E., Willam K., 2001. On the formulation of anisotropic elastic degradation. I. Theory based on a pseudologarithmic damage tensor rate. Int. J. Solids and Structures, 38, 491-518.
  • Carol I., Rizzi E., Willam K., 200 I. On the formulation of anisotropic elastic degradation. II. Generalized pseudo-Rankine model for tensile damage. Int. J. Solids and Structures, 38, 519-546.
  • Celentano D.J., Chaboche J.L., 2007. Experimental and numerical characterization of damage evolution in Steels. Int. J. Plasticity, 23, 1739-1762.
  • Chaboche J.L., Kruch S., Maire J.-F., Pottier T., 2001. Towards a micromechanics based inelastic and damage modeling of composites. Int. J. Plasticity, 17,411-439.
  • Chaboche J.L., Lesne P.M., Maire I.F., 1994. Phenomenological damage mechanics of brittle materials with description of the unilateral effects. In: Bazant ZP, Bittner Z, Jirasek M, Mazars J. Fracture and damage in quasi-brittle structures, E & FN SPON, London, 75-84.
  • Chaboche J.L., Maire J.F., 2001. A new micromechanics based CDM model and its application to CMCs. Aerospace Science and Technology, 6, 131-145.
  • Chaboche J.L., Maire J.F., 2001. New progress in micromechanics-based CDM models and their application to CMCs. Composites Science and Technology, 61, 2239-2246.
  • Chan L.C., Lee T.C., Fan J.P., Tang C.Y., 2000. Formulation of a Strain Based Orthotropic Elasto-Plastic Damage Theory. International Journal of Damage Mechanics, 9, 174-191.
  • Chandrakanth S., Pandey P.C., 1998. Damage coupled elasto-plastic nite element analysis of a Timoshenko layered beam. Computers and Structures, 69, 411-420.
  • Cheng H.H., Dusseault M.B., 2004. A Continuum Damage Mechanics Model For Geomaterials. Int. J. Rock Mech. Min. Sci., Vol. 41, No.3, SINOROCK2004 Symposium.
  • Chow C.L., Wang J., 1987. An anisotropic theory of continuum damage mechanics for ductile fracture. Engineering Fracture Mechanics, 27, 547-558.
  • Chiarelli A.S., Shao J.F., Hoteit N., 2003. Modeling of elastoplastic damage behavior of a claystone. Int. I. Plasticity, 19, 23-45.
  • Cicekli U., Voyiadjis G.Z., Abu AI-Rub R.K., 2007. A plasticity and anisotropic damage model for plain concrete. Int. J. Plasticity, 23, 1874-1900.
  • Comi C., Perego U., 2001. Fracture energy based bi-dissipative damage model for concrete. Int. J. Solids and Structures, 38,6427-6454.
  • Conil N., Djeran-Maigre J., Cabrillac R., Su K., 2004. Thermodynamics modelling of plasticity and damage of argillite. C. R. Mecanique, 332, 841-848.
  • Conil N., Djeran-Maigre J., Cabrillac R., 2004. Poroplastic damage model for claystones. Applied Clay Science, 26, 473-487.
  • Contrafatto L., Cuomo, M., 2006. A framework of elastic-plastic damaging model for concrete under multiaxial stress states. Int. J. Plasticity, 22, 2272-2300.
  • Desmorat R., Gatuingt E, Ragueneau E, 2007. Nonlocal anisotropic damage model and related computational aspects for quasi-brittle materials. Engineering Fracture Mechanics, 74, 1539-1560.
  • Desmorat R., Cantoumet S., 2008. Modeling Microdefects Closure Effect with Isotropic/Anisotropic Damage. International Journal of Damage Mechanics, 17, 65-96.
  • Desmorat R., Ragueneau E, Pham H., 2007. Continuum damage mechanics for hysteresis and fatigue of quasi-brittle materials and structures. Int. J. Numer. Anal. Meth. Geomech., 31, 307-329.
  • Dragon A., Halm D., De'soyer Th., 2000. Anisotropic damage in quasibrittle solids: modelling, computational issues and application. Comput. Meth. Appl. Mech. Eng., 183:331-52.
  • Dragon A, Mroz Z., 1979. A continuum model for plastic-brittle behavior of rock and concrete. Int. J. Engineering Science, 17, 121-137.
  • Einav I., Houlsby G.T., Nguyen G.D., 2007. Coupled damage and plasticity models derived from energy and dissipation potentials. Int. J. Solids and Structures, 44: 2487-2508.
  • Faria R., Oliver J., Cervera M., 1998. A strain-based plastic viscous-damage model for massive concrete structures. Int. J. Solids and Structures, 35, 1533-1558.
  • Faria R., Oliver J., Cervera M., 2000. On isotropic scalar damage models for the numerical analysis of concrete structures. CIMNE Monograph, No. 198, Barcelona, Spain.
  • Gatelier N., Pellet E, Loret 8., 2002. Mechanical damage of an anisotropic rock under cyclic triaxial tests. International Journal of Rock Mechanics and Mining Sciences, 39(3), 335-354.
  • Gatuingt E, Pijaudier-Cabot G., 2002. Coupled damage and plasticity modeling in transient dynamic analysis of concrete. Int. J. Numer. Anal. Methods Geomech., 26, 1-24.
  • Golshani A, Oda M., Okui Y, Takemura T., Munkhtogoo E., 2007. Numerical simulation of the excavation damaged zone around an opening in brittle rock. Int. J. Rock Mechanics & Mining Sciences, 44: 835-845.
  • Grassl P., Jirasek M., 2006. Damage-plastic model for concrete failure. Int. J. Solids and Structures, 43, 7166-7196.
  • Grassl P., Jirasek M., 2006. Plastic model with non-local damage applied to concrete. Int. J. Numer. Anal. Meth. Geomech., 30,71-90.
  • Halm D., Dragon A., 1996. A model of anisotropic damage by mesocrack growth; unilateral effect. Int. J. Damage Mechanics, 5, 384-402.
  • Halm, D., Dragon, A., 1998. An anisotropic model of damage andfrictional slidingfor brittle materials. Eur. J. Mech-N Solids, 17, 439-60.
  • Hammi Y, Horstemeyer M.E, 2007. A physically motivated anisotropic tensorial representation of damage with separate functions for void nucleation, growth and coalescence. Int. J. Plasticity, 23, 1641-1678.
  • Hansen N.R., Schreyer H.L., 1994. A thermodynamically consistent framework for theories of elastoplasticity coupled with damage. Int. J. Solids and Structures, 31, 359-389.
  • Herrmann G., 2007. A thermodynamic theory of damage in elastic inorganic and organic solids. Arch. Appl. Mech., 77, 123-33.
  • Homand-Etienne E, Hoxha D., Shao J.E, 1998. A continuum damage constitutive law for brittle rocks. Computers and Geotechnics, 22, 135-151.
  • Hayakawa H., Murakami S., 1997. Thermodynamical modeling of elastic-plastic damage and experimental validation of damage potential. Int. J. Damage Mechanics, 6, 333-363.
  • Ibijola E.A., 2002. On some fundamental concepts of Continuum Damage Mechanics. Comput. Methods Appl. Mech. Engrg., 191, 1505-1520.
  • Ibrahimbegovic A. Jehel P., Davenne L., 2008. Coupled damage-plasticity constitutive model and direct stress interpolation. Comput. Mech., 42, I-II.
  • Jason L., Pijaudier-Cabot G., Huerta A., Crouch R., Ghavamian S., 2004. An elastic plastic damage formulation for the behavior of concrete. In: Li V., Leung C.K.Y., William KJ., Billington S.L., (Eds), Fracture Mechanics of Concrete Structures, pp. 549-556.
  • Ju J.W., 1989. On energy-based coupled elastoplastic damage theories: constitutive modeling and computational aspects. Int. J. Solids and Structures, 25, 803-833.
  • Jirasek M., Patzak 8., 2002. Consistent tangent stiffness for non local damage models. Computers and Structures, 80, 1279-1293.
  • Kattan P.I., Voyiadjis G.Z., 2002. Damage mechanics with finite elements, practical applications with Computer tools. Springer, Berlin.
  • Klisinski M., Mroz Z., 1988. Description of inelastic deformation and degradation of concrete. Int. J. Solids and Structures, 24, 391-416.
  • Lammer H., Tsakmakis C., 2000. Discussion of coupled elastoplasticity and damage constitutive equations for small and finite deformations. Int. J. Plasticity, 16,495-523.
  • Lemaitre J., 1971. Evaluation of dissipation and damage in metals. Proc. I.C.M., Vol. I, Kyoto, Japan.
  • Lemaitre J., Desmorat R., 2005. Engineering Damage mechanics. Springer, Berlin.
  • Lemaitre J., Sermage J.P., Desmorat R., 1999. A two scale damage concept applied to fatigue. Int. J. Fracture, 97, 67-81.
  • Lee J., Fenves G.L., 1998. Plastic-damage model for cyclic loading of concrete structures. Journal of Engineering Mechanics Division, ASCE, 124, 892-900.
  • Li Q.M., 2000. Energy correlations between a damaged macroscopic continuum and its sub-scale. International Journal of Solids and Structures, 37, 4539-4556.
  • Lubrada V.A., Krajcinovic D., 1995. Some fundamental issues in rate theory of damage-elastoplasticity. Int. J. Plasticity, 11,763-797.
  • Mazars J., 1984. Application de la me’canique de lendommagement au comportement nonline'aire et a la rupture du be'ton de structure. The'se de Doctorat d_ Etat, L.M.T., Universite' Paris, France.
  • Mazars J., 1985. A model of unilateral elastic damageable material and its application to concrete. In: Proceedings of the RILEM International Conference on Fracture Mechanics of Concrete, Lausanne, Switzerland, Elsevier, New York, N. Y. J.
  • Mazars J., Pijalldier-Cabot G., 1989. Continuum damage theory-Application to concrete. J. Eng. Mech., 115, 345-65.
  • Menzel A., Ekh M., Runesson K., Steinmann P., 2005. A framework for multiplicative elastoplasticity with kinematic hardening coupled to anisotropic damage. Int. J. Plasticity, 21, 397-434.
  • Menzel A., Ekh M., Steinmann P., Runesson K., 2002. Anisotropic damage coupled to plasticity: Modelling based on the e_ective con-guration concept. Int. J. Numer. Meth. Engng., 54, 1409-1430.
  • Nguyen G.D., Houlsby G.T., 2008. A coupled damage-plasticity model for concrete based on thermodynamic principles: Part I: model formulation and parameter identification. Int. J. Numer. Anal. Meth. Geomech., 32, 353-389.
  • Nguyen G.D., Houlsby G.T., 2008. A coupled damage-plasticity model for concrete based on thermodynamic principles: Part II: non-local regularization and numerical implementation. Int. J. Numer. Anal. Meth. Geomech. 32:391413.
  • Ortiz M., 1985. A constitutive theory for inelastic behaviour of concrete. Mechanics of Materials, 4, 67-93.
  • Pellet E, Hajdu A., Deleruyelle F., Besnus E, 2005. A viscoplastic model including anisotropic damage for the time dependent behaviour of rock. Int. J. Numer. Anal. Meth. Geomech., 29, 941-970.
  • Pirondi A., Bonora N., Steglich D., Brocks w., Hellmann D., 2006. Simulation of failure under cyclic plastic loading by damage models. Int. J. Plasticity, 22, 2146-2170.
  • Salari M.R., Saeb S., Willam K.J., Patchet SJ., Carrasco R.C., 2004. A coupled elastoplastic damage model for geomaterials. Computer methods in applied mechanics and engineering, 193, 2625-2643.
  • Shao J.F., Chau K.T., Feng X.T., 2006. Modeling of anisotropic damage and creep deformation in brittle rocks. Int. J. Rock Mechanics & Mining Sciences, 43, 582-592.
  • Shao J.F., Hoxha D., Bart M., Homand F., Duveau G., Souley M., Hoteit N., 1999. Modelling of induced anisotropic damage in Granites. Int. J. Rock Mechanics & Mining Sciences, 36, 1001-1012.
  • Shao J.F., Jia Y, Kondo D., Chiarelli A.S., 2006. A coupled elastoplastic damage model for semi-brittle materials and extension to unsaturated conditions. Mechanics of Materials, 38, 218-232.
  • Shao J.F., Zhou H., Chau K.T., 2005. Coupling between anisotropic damage and permeability variation in brittle rocks. Int. J. Numerical and Analytical Methodes in Geomechanics, 29, 1231-1247.
  • Simo J.C., Ju J.W., 1987. Stress and strain based continuum damage models, parts 1 and II. Int. J. Solis & Structures, 23, 821-869.
  • Sterpi D., 1999. An analysis of geotechnical problems involving strain soflening effects. Int. J. Numerical and Analytical Methodes in Geomechanics, 23, 1427-1454.
  • Tao X., Phillips D.V, 2005. A simplified isotropic damage model for concrete under bi-axial stress states. Cement & Concrete Composites, 27, 716-726.
  • Thionnet A, Renard J., 1999. Modelling unilateral damage effect in strongly anisotropic materials by the introduction of the loading mode in damage mechanics. Int. J. Solids Struct., 36, 4269-87.
  • Varas F., Alonso E., Alejano L.R., Fdez.-Mam'n G., 2005. Study of bifurcation in the problem of unloading a circular excavation in a strain-soflening material. Tunnelling and Underground Space Technology, 20, 311-322.
  • Voyiadjis G., Dorgan RJ., 2007. Framework using functional forms of hardening internal state variables in modeling elasto-plastic-damage behavior. Int. J. Plasticity, 23, 1826-1859.
  • Voyiadjis G., Park T., 1999. The kinematics of damage for finite-strain elasto-plastic solids. Int. J. Engrg. Science, 37, 803-830.
  • Voyiadjis G., Taqieddin Z.N., Kattan P.J., 2008. Anisotropic damage-plasticity for concrete. Int. J. Plasticity 24, 19461965.
  • Wu J.Y, Li J., Faria R., 2006. An energy release rate-based plastic-damage model for concrete. Int. J. Solids and Structures, 43, 583-612.
  • Yazdani S., Schreyer H.L., 1988. An anisotropic damage model with dilation for concrete. Mechanics of Materials, 7, 231-244.
  • Zhu Q.Z., Shao J.F., Kondo D., 2008. A micromechanics-based non-local anisotropic model for unilateral damage in brittle materials. C. R. Mecanique, 336, 320-328.
  • Zhou H., Jia Y, Shao J.F., A unified elastic-plastic and viscoplastic damage model for quasi-brittle rocks. Int. J. Rock Mechanics & Mining Sciences. In press.
  • Zolochevsky A., Yeseleva E., Ehlers W., 2005. An anisotropic model of damage for brittle materials with different behavior in tension and compression. Forschung im Ingenieurwesen, 69, 170-180.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BPZ5-0008-0040
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.