Soils can rarely be described as ideally elastic or perfectly plastic and yet simple elastic and plastic models form the basis for the most traditional geotechnical engineering calculations. With the advent of cheap powerful computers the possibility of performing analyses based on more realistic models has become widely available. One of the aims of this book is to describe the basic ingredients of a family of simple elastic-plastic models of soil behaviour and to demonstrate how such models can be used in numerical analyses. Such numerical analyses are often regarded as mysterious black boxes but a proper appreciation of their worth requires an understanding of the numerical models on which they are based. Though the models on which this book concentrates are simple, understanding of these will indicate the ways in which more sophisticated models will perform.

A rate-independent constitutive model for natural clays is presented, formulated within the framework of kinematic hardening with elements of bounding surface plasticity. The modelling framework is intended to include effects of damage to structure caused by irrecoverable plastic strains caused by sampling, laboratory testing, or geotechnical loading. The incorporation of a structure measure allows the size of the bounding surface to decay with plastic deformations. This model can be seen as a logical extension from the Cam-clay model. The steady fall of stiffness with strain towards the Cam-clay value is controlled by a particular interpolation function. This ensures a smooth degree of approach between a kinematically hardening bubble (which is the boundary of the elastic region) and the bounding surface during their relative translation with stress history. The model describes the essential phenomena of pre-failure behaviour of natural clays: stiffness variation with strain, volumetric change accompanying distortion, peak strength at small strains. Illustrative numerical results for common geotechnical experiments on a low-sensitivity Swedish clay demonstrate the potential of the proposed model.

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A simple model is described which is able to represent the mechanical behaviour of granular soils over a wide range of void ratios and mean stresses (neglecting grain crushing). The model combines Mohr–Coulomb failure, critical states, dependence of strength and stiffness on the state parameter, a hyperbolic law for plastic stiffness degradation and a flow rule similar to that of Cam Clay. The model is formulated within the framework of kinematic hardening and bounding-surface plasticity. The model requires two elastic and eight plastic parameters which are linked to clear physical features of the mechanical response. The formulation and numerical implementation are eased by making use of a 'normalized' stress space in which the stress– strain response shows no strain softening. The model is validated by comparison with experimental results obtained from triaxial tests on Hostun sand covering a wide range of density and stress level. Some proposals are made for possible future developments of the model within the same underlying framework. Nous décrivons ici un modèle simple capable de représenter le comportement mécanique des sols granuleux sur une vaste gamme de taux de pores et de contraintes moyennes (sans tenir compte de l'écrasement des grains). Ce modèle combine la défaillance Mohr-Coulomb, les états critiques, l'assujettissement de la force et de la rigidité au paramàtre d'état, une loi hyberbolique pour la dégradation de rigidité plastique et une règle ďécoulement similaire à celle de Cam-Clay. Le modèle est formulé dans le cadre du durcissement cinématique et de la plasdcité de surface limite. Le modèle demande deux paramètees èlastiques et huit paramètees plastiques qui sont liés à des caractérisdques physiques claires de la réponse mécanique. La formulation et la mise en oeuvre numérique àsont facilitées par ľutilisation ďun espace de contrainte 'normalise' dans lequel la réponse contrainte-dé;formation ne montre aucun amollissement dû à la déformation. Le modèle est validé par une comparaison avec les résultats expérimentaux obtenus àla suite ďessais sur trois axes sur du sable de Hostun couvrant une vaste gamme de densités et de niveaux de contrainte. Nous proposons certaines possibilités de développement du modèle à ľintérieur du même cadre de travail.

SUMMARYAlthough there is a large number of constitutive models for sand available in the literature it is believed that a fresh approach, striking a balance between complexity and theoretical rigour, is desirable.The approach here has certain conceptual links with the Cam Clay series of elastic-plastic models, but includes the more general starting assumption that the yield function, plastic potential and failure locus should be given quite distinct mathematical expressions. Possible physical bases for the proposed forms are discussed.Ways in which the parameters required to define the model may be determined are suggested and the use of the model is then demonstrated. Firstly, it is shown that, where a limited set of experimental data is available, the model is flexible enough to be able to match the test results. Secondly, it is shown that, where a wide range of test results has been produced, it is possible to determine the model constitutive parameters from a small number of tests and proceed to make satisfactory predictions for other, quite different, types of test.The model is developed for sand at a single initial density, but the way in which the constitutive parameters might be expected to vary with density is discussed. The model is described for conditions of triaxial compression, and extension to more general stress states will be needed before it can be put to the test of incorporation in, for example, a finite element program.