The theory of granular packings as a chapter of the soil mechanics subject

Calixtro Yanqui

Dans les comptes rendus d’articles de la conférence: GEO2011: 64th Canadian Geotechnical Conference, 14th Pan-American Conference on Soil Mechanics and Geotechnical Engineering, 5th Pan-American Conference on Teaching and Learning of Geotechnical Engineering

Session: Teaching & Learning of Geotechnical Education

ABSTRACT: Soils are discontinuous substances made of individual solid particles and voids, defined by their contacts. Therefore, the natural description of soils is better accomplished by using granular packings. In this context, to achieve the maximum mathematical simplicity, a grain is represented by a sphere whose diameter is equal to the centroidal distance between two grains in contact, and the fundamental element, by the parallelepiped drawn by the centroides of eight neighbouring spheres, which must be in statically equilibrium, whose solid volume is obviously equal to the volume of the effective grain, and whose geometric parameters define the structure of the assembly, as well as the total volume. For the simplest granular packing, the Wadell´s shape coefficient and the Hazen´s uniformity coefficient are redefined. Under these considerations, it is settled down the fundamental equation that relates any global parameter, such as the void ratio or the volume ratio, with the structural parameters of the element. This connection is used to explain and calculate the physical and mechanical properties of soils; for instance, the relationship between the densest state and the loosest state, the relationship between the angle of internal friction and the coefficient of lateral stress "at rest", the relationship between that angle and the porosity, and the value of the Casagrande´s critical void ratio, among others. All relationships so obtained fit very well with the experimental data reported by worldwide authors.

RESUMEN: Los suelos son sustancias discontinuas conformadas por partículas sólidas y poros, definidos por sus contactos. En consecuencia, la descripción natural de los suelos se consigue de una mejor manera usando los ensambles granulares. En este contexto, para conseguir la máxima simplificación matemática, un grano se representa por una esfera cuyo diámetro is igual a la distancia centroidal entre dos granos en contacto y el elemento fundamental, por el paralelelpípedo dibujado por los centroides de ocho esferas vecinas, las cuales deben estar en equlibrio estático, cuyo volumen es obviamente igual al volumen del grano efectivo, y cuyos parámetros geométricos definen la estructura del ensamblaje, así como el volumen total. Para una ensamble granular simple, se redefinen el coeficiente de forma de Wadell y el coeficiente de uniformidad de Hazen. Bajo estas consideraciones, se establece la ecuación fundamental que relaciona cualquier parámetro global, como el índice de poros o el indice volumétrico con los parámetros estructurales del elemento. Esta relación se usa para explicar y calcular las propiedades físicas y mecánicas del suelo; por ejemplo, la realación entre los estados más denso y más suelto, la relación entre el ángulo de rozamiento interno y el coeficiente de esfuerzo lateral « en reposo », la relación entre aquel ángulo y la porosidad, y el valor del índice de poros crítico de Casagrande, entre otras. Todas estas relaciones así obtenidas se ajustan bien a los datos experimentales reportados por autores de todo el mundo. 1 INTRODUCTION oil is inherently a particulate system. Indeed, the science that treats the stress-strain behavior of soil may well be thought of as particulate mechanics (Lambe and Whitman, 1969). The way out of the difficulty lies in dropping the old fundamental principles and starting again from the elementary fact that the sand consists of individual grains920). Statements of this kind have been made several times by prominent authors. Therefore, it is compulsory to introduce some granular model in the Soil Mechanics to grasp its particulate nature. Being a branch of the physical science, this model must exhibit three merits: comprehensiveness, predictive power and simplicity (e.g. Brancazio, 1975). Within this frame of reference, a new chapter of the soil mechanics subject is proposed to rationally explain the changes of porosity, the extreme states of compactness, the transmission of simple stresses, the shear strength, and the critical state of granular soils. But the model to be outlined in this report is applicable to fine soils as well, to explain quantitatively the flocculation of silty grains, the polarization of clay sheets, the effect of the adsorbed double layer, the nature of Atterberg limits, among other topics that shall not be treated here. 2 THEORY OF GRANULAR PACKINGS Soil is a discontinuous substance made of an assemblage of grains and pores. Grains are solid bodies arbitrary in size, shape, orientation and surface texture. Pores are the space where there are no grains and may contain air and water. Grains are interconnected through almost punctual contacts, forming a highly complex and generally random system, referred to as soil structure. From the practical point of view, two features are most important in the description of the soil: the shape and the gradation of the grains. A granular packing is an orderly regular array of

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