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SUMMARYA unified constitutive model for unsaturated soils is presented in a critical state framework using the concepts of effective stress and bounding surface plasticity theory. Consideration is given to the effects of unsaturation and particle crushing in the definition of the critical state. A simple isotropic elastic rule is adopted. A loading surface and a bounding surface of the same shape are defined using simple and versatile functions. The bounding surface and elastic rules lead to the existence of a limiting isotropic compression line, towards which the stress trajectories of all isotropic compression load paths approach. A nonassociated flow rule of the same general form is assumed for all soil types. Isotropic hardening/softening occurs due to changes in plastic volumetric strains as well as suction for some unsaturated soils, enabling the phenomenon of volumetric collapse upon wetting to be accounted for. The model is used to simulate the stress-strain behaviour observed in unsaturated speswhite kaolin subjected to three triaxial test load paths. The fit between simulation and experiment is improved compared to that of other constitutive models developed using conventional Cam-Clay-based plasticity theory and calibrated using the same set of data. Also, the model is used to simulate to a high degree of accuracy the stress-strain behaviour observed in unsaturated Kurnell sand subjected to two triaxial test load paths and the oedometric compression load path. For oedometric compression theoretical simulations indicate that the suction was not sufficiently large to cause samples to separate from the confining ring.

A new bounding surface constitutive model for sands is presented and is suited to a wide range of stresses, including those sufficient to cause particle crushing. The basic concepts of critical state soil mechanics are shown to be valid, and a uniquely shaped critical state line is defined to capture the three modes of plastic deformation observed across a wide range of stresses, including particle rearrangement, particle crushing, and pseudoelastic deformation. A limiting isotropic compression line is separated from the critical state line in the υ − ln ′ p plane by a constant shift along an elastic unload-reload line. In the deviator stress -mean effective stress (q-p′) plane, the loading and bounding surfaces are homologous about the origin and defined by a simple and versatile function. Isotropic hardening and softening of the loading and bounding surfaces are controlled by plastic volumetric strains. A commonly used nonassociative flow rule is adopted. Experimental results of monotonically loaded drained and undrained triaxial tests, isotropic compression tests, and oedometric compression tests are presented for a quartz sand and used to calibrate the model. Membrane penetration is accounted for in the model simulations of the test results. A single set of material parameters is introduced enabling rigorous and accurate predictions of stress-strain behaviour in sands. Résumé :On présente un nouveau modèle constitutif de surface limite pour les sables qui convient à une large plage de contraintes incluant celles suffisantes pour produire le broyage des grains. On montre que les concepts de base de la mécanique des sols de l'état critique sont valides et on définit une ligne d'état critique de forme unique pour couvrir les trois modes de déformation plastique observés sur une large plage de contraintes incluant le réarrangement de particules, le broyage de particules, et la déformation pseudo-élastique. Une ligne limite de compression isotrope est sé-parée de la ligne d'état critique dans le plan υ − ln ′ p par un déplacement constant le long de la ligne déchargement-rechargement élastique. Dans le plan q-p′ les surfaces de chargement et surfaces limites sont homologues autour de l'origine et sont définies par une fonction simple et versatile. Le durcissement-ramollissement isotrope du chargement et les surfaces limites sont contrôlés par des déformations plastiques volumétriques. On a adopté une loi d'écoulement non-associative communément utilisée. On présente les résultats expérimentaux d'essais de compression monotonique triaxiale isotrope drainée et non drainée et d'essais de compression oedométrique pour un sable de quartz utilisé pour calibrer le modèle. On tient compte de la pénétration de la membrane dans les simulations du modèle des résultats d'essais. On introduit un simple ensemble de paramètres de matériau permettant des prédictions rigoureuses et précises du comportement contrainte-déformation des sables.

The problem of cavity expansion in unsaturated soils is investigated. A unified constitutive model formulated in a critical state framework using the concepts of effective stress and bounding surface plasticity theory is adopted. Consideration is given to the effects of suction and particle crushing in the definition of the critical state and the evolution of the bounding surface. The model accurately captures stress-strain behaviour for a range of load paths encompassing that experienced by soils during cavity expansion. Specifically, the similarity technique is used to solve the cavity expansion problem in speswhite kaolin and Kurnell sand. Eight governing equations are defined and solved simultaneously as an initial value problem including an equilibrium equation for stresses around the cavity. Cylindrical and spherical cavities are considered, as are constant suction and constant moisture content conditions. Substantial differences in the stress-strain response of saturated and unsaturated soils surrounding expanding cavities are observed. The paper highlights the major influence of suction and the importance of accounting for this when using cavity expansion theory to interpret results of the cone penetration and pressuremeter tests.

SUMMARYThe expansion of cylindrical and spherical cavities in sands is modelled using similarity solutions. The conventional Mohr-Coulomb failure criterion and the state parameter sand behaviour model, which enables hardeningÀsoftening, are used in the analysis. The sand state is defined in terms of a new critical state line, designed to account for the three different modes of compressive deformation observed in sands across a wide range of stresses including particle rearrangement, particle crushing and pseudoelastic deformation. Solutions are generated for cavities expanded from zero and finite radii and are compared to those solutions where a conventional critical state line has been used. It is shown that for initial states typical of real quartz sand deposits, pseudoelastic deformation does not occur around an expanding cavity. Particle crushing does occur at these states and causes a reduction in the stress surrounding the cavity. This has major implications when using cavity expansion theory to interpret the cone penetration test and pressuremeter test.

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SUMMARY Based on hypotheses derived directly from experimental observations of the triaxial behaviour, a constitutive model for fibre reinforced sands is built in this paper. Both the sand matrix and the fibres obey their own constitutive law, whereas their contributions are superimposed using a volumetric homogenization procedure. The Severn‐Trent sand model, which combines well‐known concepts such as critical state theory, Mohr‐Coulomb like strength criterion, bounding surface plasticity and kinematic hardening, is adopted for the sand matrix. Although the fibres are treated as discrete forces with defined orientation, an equivalent continuum stress for the fibre phase is derived to allow the superposition of effects of sand and fibres. The fibres are considered as purely tensile elements following a linear elastic constitutive rule. The strain in the fibres is expressed as a fraction of the strain in the reinforced sample so that imperfect bonding is assumed at the sand‐fibre interface. Only those fibres oriented within the tensile strain domain of the sample can mobilize tensile stress—the orientation of fibres is one of the key ingredients to capture the anisotropic behaviour of fibre reinforced soil that is observed for triaxial compression and extension loading. A further mechanism of partition of the volume of voids between the fibres and the sand matrix is introduced and shown to be fundamental for the simulation of the volumetric behaviour of fibre‐reinforced soils. Copyright © 2012 John Wiley & Sons, Ltd.