Modelling of induced anisotropic damage in granites J.F. Shao a, *, D. Hoxha b , M. Bart a , F. Homand b , G. Duveau a , M. Souley b , N. Hoteit c a LML-URA 1441, EUDIL-USTL, Cite Scienti®que, 59655, Villeneuve d'Ascq, France b LAEGO, ENS GeÂologie, Vandoeuvre les Nancy, France c ANDRA, Chatenay Malabry, France Accepted 8 October 1999 Abstract 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. # 2000 Elsevier Science Ltd. All rights reserved. 1. Introduction Damage by microcracking is the main dissipation process associated with inelastic behaviour and failure in most brittle materials such as rocks, concrete and ceramic composites. However, the emphasis in rock mechanics is put on material damage induced by com- pressive stresses. Many laboratory results have been reported on laboratory characterisation of initiation and growth mechanisms of microcracks as well as the impact of damage on material behaviour [1±7]. Exper- imental studies have shown that there are dierent mechanisms by which microcracks can initiate and grow under compressive stresses. Irreversible defor- mation and material failure occur by progressive ma- terial degradation as microcracks initiate and grow on a small scale and coalesce to form large scale fractures and faults. These mechanisms may include sliding along pre-existing microcracks and grain boundaries, pore crushing, elastic mismatch between mineral grains and dislocation movement. Furthermore, the micro- crack growth generally has a directional character which results in induced rock anisotropy. Another im- portant feature of deformation and failure in brittle rocks is the sub-critical growth of microcracks, leading to a time-dependent behaviour. Various physical mech- anisms of the sub-critical growth have been discussed by dierent authors, for instance [8±10]. The main pro- cess observed in most rocks is the stress corrosion phenomenon. An extensive laboratory testing program has been carried out on three representative granites (Lac du Bonnet, Vienne and Senones) in the framework of the research project jointly conducted in LAEGO (Labora- toire Environnement Ge omate riaux Ouvrages) and LML (Laboratoire de MeÂcanique de Lille). Dierent techniques (wave velocity, acoustic emission, elastic moduli evaluation and permeability) were used to characterise induced damage in these rocks [11]. Dier- ent loading paths (triaxial compression with dierent con®ning pressure, lateral extension and proportional loading) were considered. The experimental results have clearly shown the progressive growth of oriented International Journal of Rock Mechanics and Mining Sciences 36 (1999) 1001±1012 1365-1609/99/$ - see front matter # 2000 Elsevier Science Ltd. All rights reserved. PII: S1365-1609(99)00070-2 www.elsevier.com/locate/ijrmms * Corresponding author. Tel.: +33-3-2043-4626; fax: +33-3-2043- 4335. E-mail address: jian-fu.shao@eudil.fr (J.F. Shao).