Quantification of Doublet Vector Distribution of Granular Materials

Soil fabric quantities such as doublet vector and branch vector distributions are important in doublet mechanics and micromechanics modeling of soil behavior. The quantification of these quantities is therefore imperative in applying and verifying these modeling techniques. This paper presents the development of a new method to quantify the doublet distribution of granular assemblies and some experimental results. The method treated doublet vectors as random vectors and built up the integrated distribution function from the distribution functions of the projections of the random vectors in the three orthogonal subspaces. A mechanism to evaluate the doublet vector distribution from sectional images was developed for the case of granular assemblies composed of spherical or subspherical particles. A procedure was also developed to assess the integrated distribution function through evaluating the projection distribution functions in two orthogonal subspaces for the case of axialsymmetric distribution of doublet vectors of spherical particles. The comparison of the doublet distribution of a dense Ottawa sand specimen, quantified by the proposed procedure, with Odaʹs experimental observations on contact normal distributions indicated a qualitative consistency. Doublet distribution of spherical assemblies is the same as the branch vector distribution and the contact normal distribution when the nearest neighbors are in contact, and therefore can be applied in both doublet mechanics and micromechanics modeling. The developed procedure is not scale-dependent and can be used to quantify these distributions of particulate materials in different length scales.