Abstract. Fine soils are substances made of tiny particles, for which, besides their geometrical assemblage, the electrochemical forces are important. But the broad experience in Soil Mechanics has shown that, excluding the time, they behave like granular materials. By using the scanning electron microscopy, it has been shown by several authors that clay assemblages are structures of the second order, made of solid particles grouped in clusters. Applying the theory of packings of spheres in contact to the intra-cluster structure as well as to the entire mass of soil, a fundamental equation is obtained. The plastic limit is found to be a constant for a geological formation, because it is obtained by eliminating the capillary water and transforming the clay mass into a first order structure. The liquid limit is a inherently property of the second order, due to the development of clusters. Consequently, there is a linear relationship between the plasticity index and the liquid limit, with a slope of unity, as can be deduced from the abundant data reported by several authors around the world.
Abstract. In this paper, coarse soils are modeled by granular packings, because both of them have similar characteristics, such as: gaseousity, duality, dilatancy, fragility and hyperbolicity. By virtue of these properties, it is assumed that the contact force ensemble remains the same, while the packing changes because of its dual character, regarding the compactness of the soil. For the dense state, both assemblages coincide themselves, forming chains of contact forces; the transmission of stresses obeys the Trollope´s hypothesis of centroidal reactions; and the volumetric strain increases. For the loose state, the packing adopts a "passive" distribution, yielding a constant angle of internal friction at failure; so that, the strain is contractive and the stress transmission occurs fundamentally by shear, in a similar fashion to the Rowe´s mechanism. In the figures, the good correspondence between the results of the theory and the reported experimental data is shown.
The rhombic sphere packing can be used to model the biaxial test on granular soils in a very simple way. According to the angle of assemblage, the packing is dilatant or contractive. Correspondingly, overall stresses are transmitted as chains of forces or oblique forces of contact. The connection of the soil stress-strain behaviour and the packing void ratio is achieved by mapping both of the plots. The mapping shows that dense soils are dilatant and loose soils are contractive, separated by the critical state. It also shows that the bifurcation point and the peak strength are features only of dense soils. The band of strain localization is analysed in the elastic regime, and its inclination is found maximizing the intensity of the mobilized stress ratio. The stresses within the shear band are obtained by assuming a partially coaxial packing rotated to reach the full plastic state. The equilibrium of the overall stress at the line of discontinuity reveals a relationship between the peak friction angle and the coefficient of lateral pressure at rest. As long as these parameters are obtained independently of each other, they allow the validation of the theory.
Abstract. Coarse soils are substances made of grains of different shape, size and orientation. In this paper, new massivemeasurable grain indexes are defined to develop a simple and systematic theory for the ideal packing of grains. First, a linear relationship between an assemblage of monodisperse spheres and an assemblage of polydisperse grains is deduced. Then, a general formula for the porosity of linearly ordered packings of spheres in contact is settled down by the appropriated choosing of eight neighboring spheres located at the vertices of the unit parallelepiped. The porosity of axisymmetric packings of grains, related to sand piles and axisymmetric compression tests, is proposed to be determined averaging the respective linear parameters. Since they can be tested experimentally, porosities of the densest state and the loosest state of a granular soil can be used to verify the accuracy of the present theory. Diagrams for these extreme quantities show a good agreement between the theoretical lines and the experimental data, no matter the dependency on the protocols and mineral composition.
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