Micromechanical considerations of the interactions between the granular skeleton of an unsaturated granular soil and the contained moisture involve the classical interaction model consisting of a water bridge in contact with two rigid smooth spheres of equal radius, at a separation determined by their actual surface roughness, and surrounded by a gas with a vapour pressure at equilibrium with the water. In this paper the water volume and the interparticle contact force are related to the water suction, the water–solid surface contact angle, and the size and roughness of the spheres in dimensionless terms. The dimensionless water suction is also related to the corresponding relative humidity of the water vapour. The calculated equilibrium relations are shown to possess non-uniqueness, which is interpreted in terms of soil mechanical properties while recognising that for low saturations in natural processes the humidity of the pore air is the independent parameter. The developed analytical solutions show the classical toroidal approximation to be reasonable. These solutions are applied in a companion paper to clarify the concept of an intergranular stress induced by both pore suction and related surface tension.

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In experimental research into the constitutive properties of granular materials the phenomenon of membrane penetration is one of the major sources of error. For instance, in drained isotropic loading and unloading tests on medium loose fine sand the errors in the volume change due to membrane penetration can be of the order of 20% and 40% respectively. In the first stage of an undrained triaxial compression test on the same sand, when the effective isotropic stress decreases, the deviator stress can become 50% greater owing to membrane penetration; because of this a tendency towards lique faction might remain obscure. It is shown that such errors can be reduced by a factor of 5 if the proper membranes are used and if the remaining membrane effect of restraint is accounted for properly. To this end the membrane should consist of much stiffer material than latex rubber, the membrane thickness should be of the order of the mean grain size and the ratio of the mean grain size and the sample diameter should not be too large (0·003 in the case considered). For medium loose fine quartz sand the optimum value of Young's modulus for the membrane should be of the order of E≃5×107 N/m2 so that the membrane is about 40 times stiffer than latex rubber. Dans la recherche scientifique sur le comportement mécanique des sols granuleux le phénomène de la pénétration de la membrane est une des sources importantes d'erreur. Par example en cas des essais de chargement et déchargement hydrostatiques avec drainage sur un sable fine assez lâche l'erreur de la variation volumétrique par suite de la pénétration de la membrane peut monter 20% et 40% respectivement. En cas des essais de compression triaxiale sans drainage sur le même sable la tendance à liquefaction restera obscure; avant que la pression effective isotrope minimale est attenu le deviateur des contraintes peut être 50% plus grand par la pénétration de la membrane. Il est montré que cettes erreurs peuvent se réduire à un facteur de 5 pourvu que les propres membranes soient utilisés et pourvu que la contrainte de soutien de la membrane soit tenu en compte proprement. A cet effet il faut, que les membranes soient composés de matériau plus rigide que caoutchouc, que l'épaisseur soit à peu près aussi grande que le diamètre moyen des grains et que le rapport du diamètre moyen des grains et du diamètre d'échantillon soit limité (dans le cas présent=0·003). Par example le module d'élasticité de la membrane doit être environ de E ≈ 5 × 107 N/m2 pour un sable de grains fines de quartz et d'une compacité assez lâche; donc approximativement 40 fois plus rigide que cauotchouc.

The existing elasto-plastic models of geomaterials have been developed on the basis of experiments in which uniform straining was attempted. The shear bands observed in experiments have been described directly without direct relation to the elasto-plastic models. However, shear band initiation can be considered as an instability of plastic flow; consequently the material behaviour under uniform deformation and the occurrence of a shear band can be considered as coupled phenomena. In this Paper the coupling relations are elaborated and applied in the calculation of shear band initiation for a range of popular constitutive models of materials like drained clay, sand, concrete and rock. It is found that amongst the popular elasto-plastic models large variations in the predicted slope of the shear band and the predicted instant of initiation occur. Les modèles élasto-plastiques des sols existants ont été développés sur la base d'essais dans lesquels une déformation uniforme est imposée. La formation des surfaces de glissement observées dans les essais a été décrite directement sans la mettre en relation directe avec les modèles élasto-plastiques. Cependant la formation d'une surface de glissement peut être considérée comme une instabilité de fluage plastique; alors le comportement du matérial sous une déformation uniforme et la formation des surfaces de glissement peuvent être considérés comme des phénomènes couplés. Dans cet article les équations, qui traduisement cette relation, sont établies et appliquées dans un calcul de la formation d'une surface de glissement pour une série de modèles classiques de comportement de matériaux tels que argile drainée, sable, béton et roche. Il est constaté que, parmi les modèles classiques élasto-plastiques, de grandes variations existent dans les prévisions de l'inclinaison de la surface de glissement et de l'instant de son apparition.

For the saturated case with only one pore fluid, either water or air, the roles of both the intergranular stress tensor and the pore fluid stress can be distinguished easily. In the unsaturated case, the capillary water is recognized to induce capillary suction in the pores and capillary-suction-induced interparticle forces. At the macroscale, volume averaging of these forces would lead to the capillary-suction-induced intergranular stress tensor. In its approximate formulation, the concept of the fabric stress tensor is applied, enabling the effect of the spatial distribution of the intergranular fabric on the capillary water bridges as occurring in the drier pendular saturation phase to be accounted for. Subsequently, the combined intergranular stress tensor and the combined pore fluid stress tensor can be derived directly. The constitutive relation of a granular skeleton, composed of elastic particles with mainly frictional interaction, like quartz sands and silts, is considered to remain independent of the degree of saturation. Under such restrictive conditions, only the additional physical parameters of the capillary-suction-induced intergranular stress tensor need to be determined, which can be achieved by means of inverse modeling, taking advantage of all macroscale experimental data and physical modeling for the whole unsaturated range. For clays and peats, with potential physicochemical and biochemical actions and double porosity and/or fibrous microstructures, the constitutive models can be expected to be physically more complicated, thus involving more physically relevant parameters. Hence, clays and peats must be considered to fall outside the scope of the proposed model framework.Abbreviations: DEM, discrete element method.The physical relevance of the continuum mechanical measures of stress, deformation, and flow of the pore fluids and stress and deformation of the solid skeleton forms the basis of any constitutive modeling and subsequent application for predictions in geomechanics.The physical relevance of the applied continuum measures of stress, deformation, and flow is a reflection of the physical concepts as applied in their descriptions. For instance, for the fluid-saturated case, the calculation of the deformation of the solid skeleton due to a changing pore fluid stress can be achieved by applying the macroscale isotropic pore fluid stress tensor pI, at least if the substance composing the particles remains elastic. For the solid skeleton of granular materials, the intergranular stress tensor s* and a potential microstructure tensor are derived using micromechanics in combination with volume averaging, irrespective of the degree of saturation. For the unsaturated case, the effects of the two simultaneous pore fluids on the solid skeleton are limited by the conditions for the granular skeleton that its deformation remains identically dependent on the tensors of the intergranular stress and a combined measure of both pore fluid stresses, as for both saturated cases. In fact, these conditions ...