1 INTRODUCTION
This study is aimed at formulating a general elastic/viscoplastic non associated constitutive equation for a stratified sedimentary rock : Tournemire shale. This rock can be idealized as transversely isotropic, the plane of isotropy being the bedding plane. The dependence of the elastic moduli on the stress state is expressed in terms of the invariants of the stress tensor. The viscoplatic criterion, the flow rule and a short-term failure criterion are expressed in a general invariant form. Finally the model is checked against data.
Isotropic rocks seldom occur in nature. Oriented internal structures such as oriented crystallographic axis, grains fissuration, cracks, result on the macroscopic level in a directional mechanical response of rocks. Thus, the design and stability analysis of underground excavations requires a good knowledge of the mechanical behavior of such rocks. Generally, the experimental investigations were performed on transversely isotropic rocks (Donath 1972, McLamore&Gray 1969, Allirot and Boehler 1979, Niandou 1993, etc.). These investigations led to theories able to predict the dependence of strength on - the angle between the normal to the isotropic plane and the direction of the major principal stress. A suitable framework allowing to describe both yielding and failure of anisotropic rocks with the required generality and pertinence was provided by the theory of representation of tensor functions. Invariant formulation of the perfect plastic behavior with application to stratified cohesive materials as well as for materials with internal friction have been developed by Boehler and Sawczuk (1977) and Boehler(1978,1987) using irreductible representations of tensor functions. To describe the behavior of initially anisotropic sedimentary rocks, a generalization of the Cam-Clay model has been proposed by Nova (1986) following the pioneering works of Hill (1950) and Olszack & Urbanowschi (1956). In this paper we present an elastic /viscoplastic non associated constitutive equation for a stratified sedimentary rock Tournemire shale. From the experimental investigation conducted at Lille Mechanics Laboratory (URA CNRS No 1441) on this shale (Niandou 1994), we can conclude that the variation of the mechanical characteristics with respect to the oriented structure of the material may be considered as continues. The initial anisotropy is taken into account in the structure of the yield function, in that of the flow rule and of the short term failure criterion by means of a constant anisotropic fourth order tensor. No a priori assumption is made concerning the existence of a viscoplastic potential. A procedure to determine the constitutive parameters from the data is shown. Finally, a comparison between model prediction and experimental results obtained in several triaxial tests on specimens of different orientations with respect to the major principal stress direction is presented.
A material is regarded as being orthotropic at any point in a preferred reference configuration if there exist three orthogonal planes such that the mechanical properties of the material are symmetrical with respect to each of these planes. If one of the symmetry planes is isotropic the medium is said to be transversely isotropic.
