INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS Int. J. Numer. Anal. Meth. Geomech. 2007; 31:1517–1535 Published online 7 February 2007 in Wiley InterScience (www.interscience.wiley.com). DOI: 10.1002/nag.605 Triaxial behaviour of transversely isotropic materials: Application to sedimentary rocks A. Rouabhi 1, ∗, † , M. Tijani 1 and A. Rejeb 2 1 Centre de G´ eosciences, Ecole des Mines de Paris, Fontainebleau, France 2 Institut de Radioprotection et de Sˆ uret´ e Nucl´ eaire, Fontenay-Aux-Roses, France SUMMARY Failure and long-term behaviour of oriented solids are studied. Transversely isotropic materials are considered and a mathematical formulation that respect the material symmetry is developed and applied to model the triaxial behaviour of sedimentary rocks. Two failure criteria and a viscoplastic constitutive model that describe, respectively, triaxial failure and triaxial creep tests are presented and discussed. The application of the developed models to describe the mechanical behaviour of Tournemire shale shows that theoretical predictions are in good agreement with the experimental data. In the present paper, the developed approach is applied to sedimentary rock materials, nevertheless, it can be generalized to any material that exhibits transverse isotropy. Copyright 2007 John Wiley & Sons, Ltd. Received 6 February 2006; Revised 18 December 2006; Accepted 27 December 2006 KEY WORDS: rocks; transverse isotropy; triaxial stresses; failure surface; viscoplasticity 1. INTRODUCTION Based on experimental data, different approaches have been proposed to describe the deformation and the failure behaviour of anisotropic rocks. It is not the purpose of this paper to establish an exhaustive summary of the works devoted to anisotropic solids. The present work is devoted to study the behaviour of transversely isotopic solids under triaxial loadings (failure and creep tests). We mention only some review papers addressing the state of art on the study of anisotropic materials [1–8]. Even though suitable framework allowing to establish constitutive equations for anisotropic solids that respect the material symmetry is furnished by the theory of representation for tensor functions (see, for example, References [1, 9–11]), the formulation of adequate laws, that describe the mechanical behaviour of these solids, with a reasonable number of material constants which ∗ Correspondence to: A. Rouabhi, Centre de G´ eosciences, Groupe Hydro-G´ eo-Ing´ enierie, Ecole des Mines de Paris, 35, Rue Saint-Honor´ e, 77305 Fontainebleau Cedex, France. † E-mail: ahmed.rouabhi@ensmp.fr Copyright 2007 John Wiley & Sons, Ltd.