A method to evaluate settlements and rotations of rigid shallow foundations on sand under the combined action of inclined and eccentric loads is presented. Experimental results obtained on a model strip foundation are shown first. Next, a mathematical model is formulated which is based on the hypotheses that (a) the foundation and the soil can be considered as a macro-element for which the loadings act as generalized stress variables while the displacements and rotation of the foundation are the corresponding generalized strain variables; and (b) the constitutive law of the macro-element, that is the relationship between generalized stress and strain rates, is rigid-plastic strain-hardening with a non-associated flow rule. Constitutive functions and parameters are determined by means of simple calibration tests. Predictions of the theory are then compared with experimental results in tests where loadings vary in a complex way up to foundation failure. It is shown that experimental evidence is well matched by the theory. A simplified method, for loading conditions which are far from failure, is presented. It is shown that, although the method is as simple as the elastic theory, it has the advantages of allowing the coupling of displacements and rotations to be predicted correctly. On présente une méthode pour la prédiction des tassements et des rotations des fondations superficielles rigides sur sable, soumises à l'action combinée des chargements inclinés et excentrés. On présente les résultats expérimentaux obtenus sur une semelle filante en modèle réduit. On en déduit un modèle mathématique basé sur les hypothèses suivantes: (a) la fondation et le sol peuvent être considérés comme un macroélément dont les chargements agissent comme variables des contraintes généralisées tandis que les déplacements et les rotations de la semelle sont les variables des déformations correspondants; (b) la loi constitutive pour le macroélément, c'est à dire la relation entre les incréments des contraintes et des déformations généralisées, est du type rigide-plastique écrouiss-able avec une loi de fluage non-associée. Les fonctions et les paramètres constitutis ont été déterminés à partir des essais simples de calage. Les prédictions de la théorie sont en suite comparées avec les résultats expérimentaux dans des essais où les chargements varient dans une façon complexe jusqu'à la rupture. On montre que la théorie donne des bonnes prédictions. Une méthode simplifiée est finalement présentée pour conditions de chargement qui sont loin de la rupture. Bilese que la méthode présentée soit aussi simple que la méthode élastique, on montre qu'avec elle on peut modéliser correctement le couplage entre les déplacements et les rotations tandis que cela n'est pas possible avec la méthode élastique.

The paper shows that the possibility of controlling the incremental response of a soil specimen subjected to an arbitrary loading programme is lost at a stress level which is below the value for which failure occurs in ordinary tests. The relation between this level and other critical values (bifurcation into a shear band, peak of the stress deviator in an undrained test, stability under dead load) is discussed.

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.

SUMMARYThe mechanical behaviour of bonded geomaterials is described by means of an elastoplastic strainhardening model. The internal variables, taking into account the 'history' of the material, depend on the plastic strains experienced and on a conveniently defined scalar measure of damage induced by weathering and/or chemical degradation.For the sake of simplicity, it is assumed that only internal variables are affected by mechanical and chemical history of the material. Despite this simplifying assumption, it can be shown that many interesting phenomena exhibited by weathered bonded geomaterials can be successfully described. For instance, (i) the transition from brittle to ductile behaviour with increasing pressure of a calcarenite with collapsing internal structure, (ii) the complex behaviour of chalk and other calcareous materials in oedometric tests, (iii) the chemically induced variation of the stress and strain state of such kind of materials, are all phenomena that can be qualitatively reproduced. Several comparisons with experimental data show that the model can capture the observed behaviour also quantitatively.

SUMMARYAn extended version of the classical Generalized Backward Euler (GBE) algorithm is proposed for the numerical integration of a three-invariant isotropic-hardening elastoplastic model for cemented soils or weak rocks undergoing mechanical and non-mechanical degradation processes. The restriction to isotropy allows to formulate the return mapping algorithm in the space of principal elastic strains. In this way, an efficient and robust integration scheme is developed which can be applied to relatively complex yield surface and plastic potential functions. Moreover, the proposed algorithm can be linearized in closed form, thus allowing for quadratic convergence in the global Newton iteration. A series of numerical experiments are performed to illustrate the accuracy and convergence properties of the algorithm. Selected results from a finite element analysis of a circular footing on a soft rock layer undergoing chemical weathering are then presented to illustrate the algorithm performance at the boundary value problem level.