An experimental and theoretical investigation on the behaviour of a calcarenite subjected to various axisymmetric loading programmes is reported. The essential feature of the observed behaviour is the occurrence of a destructuration phase, which marks the transition from rock-like to soil-like behaviour. During this phase the state of stress remains constant, while strains increase steadily. Three phases can be distinguished: an initial elastic, a destructuration phase and a hardening or softening phase which ends on an ultimate state locus which is linear in the p'–q plane. The observed behaviour is more and more ductile for increasing confining pressures. In the softening regime the specimen is unstable. It is shown that by means of a mathematical model based on the theory of strain-hardening plasticity it is possible to describe mathematically the overall behaviour of the calcarenite in various types of triaxial compression test. Qualitative and quantitative accuracy is generally satisfactory, especially for drained tests at high confining pressures and oedometric loading. For low confining pressures agreement between calculated and observed data after peak is much less satisfactory. KEYWORDS: calcareous soils; constitutive relations; laboratory tests; plasticity; soft rocks. L'article présente une recherche expérimentale et théorique du comportement d'une calcarénite soumise à différents programmes de chargement axisymétrique. La principale observation est l'apparition d'une phase de déstructuration correspondant à la transition entre un comportement de type roche et un comportement de type sol. Lors de cette phase, l'état de contrainte reste constant alors que les déformations augmentent réguli&gave;rement. Trois phases différentes sont à distinguer: une phase initiale élastique, une phase de déstructuration et une phase d'écrouissage positif ou négatif menant à un état ultime, représenté par une droite dans le plan p'–q. Le comportement observé devient de plus en plus ductile au fur et à mesure que la pression de confinement augmente. En régime de radoucissement, l'échantillon est instable. Un modàle mathématique fondé sur la théorie de la plasticité par écrouissage positif permet de décrire mathématiquement le comportement d'ensemble d'une calcarénite au tours de différents essais de compression triaxiaux. La précision est, dans l'ensemble, qualitativement et quantitativement satisfaisante et ce, plus particuliàrement, pour les essais drainés à forte pression de confinement et pour les essais oedométriques. Pour les faibles pressions de confinement, la correspondance entre les valeurs calculées et les valeurs mesurées après le pic est beaucoup moins bonne.

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Yield and plastic potential surfaces are often affected by problems related to convexity. One such problem is encountered when the yield surface that bounds the elastic domain is itself convex; however, convexity is lost when the surface expands to pass through stress points outside the current elastic domain. In this paper, a technique is proposed, which effectively corrects this problem by providing linear homothetic expansion with respect to the centre of the yield surface.A very compact implicit integration scheme is also presented, which is of general applicability for isotropic constitutive models, provided that their yield and plastic potential functions are based on a separate mathematical definition of the meridional and deviatoric sections and that stress invariants are adopted as mechanical quantities. The elastic predictor-plastic corrector algorithm is based on the solution of a system of 2 equations in 2 unknowns only. This further reduces to a single equation and unknown in the case of yield and plastic potential surfaces with a linear meridional section. The effectiveness of the proposed convexification technique and the efficiency and stability of the integration scheme are investigated by running numerical analyses of a notoriously demanding boundary value problem.

In this paper, it is mathematically demonstrated that classical yield and failure criteria such as Tresca, von Mises, Drucker-Prager, Mohr-Coulomb, MatsuokaNakai and Lade-Duncan are all defined by the same equation. This can be seen as one of the three solutions of a cubic equation of the principal stresses and suggests that all such criteria belong to a more general class of non-convex formulations which also comprises a recent generalization of the Galileo-Rankine criterion. The derived equation is always convex and can also provide a smooth approximation of continuity of at least class C 2 of the original Tresca and Mohr-Coulomb criteria. It is therefore free from all the limitations which restrain the use of some of them in numerical analyses. The mathematical structure of the presented equation is based on a separate definition of the meridional and deviatoric sections of the graphical representation of the criteria. This enables the use of an efficient implicit integration algorithm which results in a very short machine runtime even when demanding boundary value problems are analysed.