Modelling of induced anisotropic damage in granites

This paper deals with numerical modelling of induced damage in three granites. A continuous anisotropic damage model is proposed in the framework of thermodynamics and fracture mechanics. A second rank tensor is used to describe damage state which is directly related to orientation and density of microcracks. Both time independent and time dependent (or sub-critical) growth of microcracks are taken into account. A simple procedure for the determination of model parameters from standard laboratory tests is proposed. Comparisons between model simulation and experimental data are presented for some basic loading paths. Finally the application of the model to stability analysis of the Mine-by test tunnel of the URL in Manitoba (Canada) is presented. A comparison between numerical predictions and in situ observations makes it possible to evaluate the performance of the proposed model.

[1]  Sia Nemat-Nasser,et al.  A Microcrack Model of Dilatancy in Brittle Materials , 1988 .

[2]  S. Nemat-Nasser,et al.  Micromechanics: Overall Properties of Heterogeneous Materials , 1993 .

[3]  J. Ju,et al.  Micromechanical Damage Models for Brittle Solids. Part I: Tensile Loadings , 1991 .

[4]  J. Ju,et al.  Micromechanical Damage Models for Brittle Solids. Part II: Compressive Loadings , 1991 .

[5]  D. Muir Wood,et al.  Localisation and bifurcation theory for soils and rocks , 1998 .

[6]  Zdeněk P. Bažant,et al.  Tangential stiffness of elastic materials with systems of growing or closing cracks , 1997 .

[7]  André Dragon,et al.  A Model of Anisotropic Damage by Mesocrack Growth; Unilateral Effect , 1996 .

[8]  Jean Lemaitre,et al.  A Course on Damage Mechanics , 1992 .

[9]  Philip G. Meredith,et al.  4 – THE THEORY OF SUBCRITICAL CRACK GROWTH WITH APPLICATIONS TO MINERALS AND ROCKS , 1987 .

[10]  John A. Hudson,et al.  Comprehensive rock engineering , 1993 .

[11]  Surendra P. Shah,et al.  Toughening Mechanisms in Quasi-Brittle Materials , 1991 .

[12]  J. Lemaitre,et al.  Mécanique des matériaux solides , 1996 .

[13]  B. Atkinson Fracture Mechanics of Rock , 1987 .

[14]  B. Budiansky,et al.  Elastic moduli of a cracked solid , 1976 .

[15]  P. A. Cundall,et al.  NUMERICAL MODELLING OF DISCONTINUA , 1992 .

[16]  Jian-Fu Shao,et al.  A continuum damage constitutive law for brittle rocks , 1998 .

[17]  Mark Kachanov,et al.  Elastic Solids with Many Cracks and Related Problems , 1993 .

[18]  John M Kemeny,et al.  Micromechanics of Deformation in Rocks , 1991 .

[19]  P. Steif Crack extension under compressive loading , 1984 .

[20]  L. S. Costin,et al.  Damage mechanics in the post-failure regime , 1985 .

[21]  J. Fredrich,et al.  Micromechanics of the brittle to plastic transition in Carrara marble , 1989 .

[22]  P. A. Cundall,et al.  Modeling notch-formation mechanisms in the URL Mine-by Test Tunnel using bonded assemblies of circular particles , 1998 .

[23]  Michael F. Ashby,et al.  The failure of brittle porous solids under compressive stress states , 1986 .

[24]  Dusan Krajcinovic,et al.  A micromechanical model for concrete in compression , 1988 .

[25]  W. R. Wawersik,et al.  Post-failure behavior of a granite and diabase , 1971 .

[26]  Dusan Krajcinovic,et al.  Damage tensors and the crack density distribution , 1993 .

[27]  Françoise Homand,et al.  Distinct Element Modelling of An Underground Excavation Using a Continuum Damage Model , 1998 .

[28]  Teng-fong Wong,et al.  MICROMECHANICS OF FAULTING IN WESTERLY GRANITE , 1982 .

[29]  J. Ju,et al.  On energy-based coupled elastoplastic damage theories: Constitutive modeling and computational aspects , 1989 .

[30]  J. Fredrich,et al.  Micromechanics of thermally induced cracking in three crustal rocks , 1986 .

[31]  Zvi Hashin,et al.  The differential scheme and its application to cracked materials , 1988 .