The theory of granular packings for fine soils

Abstract

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.

Granular mechanics of normally consolidated fine soils

“…The strain of the basic cell whose vertexes are the center of the contact spheres, considered for the moment to be rigid, may be described in terms of the azimuth angles of assemblage, regarding the principle of multiplicity of packings. In this path, it has been established that the rhombohedron is the appropriate lattice for studying the clay behavior [3].…”

“…Because its kinematics is ease to understand, the distortional or shearing packing of contact spheres is to be described in some detail ( Fig.1). Once the relationship between the voluminosity, υ, and the azimuth angle β of the line of contact is established [3], the change of volume with the shearing strain is obtained as its derivative:…”

“…In this case, the basic cell must meet the conditions of axial symmetry and large elongation. This happens when the principal diagonal of the rhombohedron is vertical, and its eight spheres occupy four horizontal layers [3]. The change of volume may be related to the axial shearing strain through the equation:…”

“…Therefore, for the critical state, the contractive soil can be described by using the hypothesis and methods of dilative soils. So this, the entire geological formation is described by the equation [3]:…”

“…As occurs with sands, this peculiar behavior of clays is a consequence of their particulate nature. So that, normally consolidated and lightly overconsolidated clays may be analyzed by means of the theory of granular packings, having account of the second order of their structure, for what υ1 is the packing of clay particles and υ 2 , the packing of clusters [3…”