Random field modeling of the void phase of soils

Abstract

The elements of a formal probabilistic characterization of the two-phased microstructure of a particulate random medium such as granular soil are described. First, the medium is idealized, within a region considered statistically homogeneous and isotropic, as a random arrangement of solid spheres of different sizes. In terms of the local-mean porosity and six characteristic particle sizes related to the moments of the grain size distribution, an efficient statistical description is possible of the complex geometry of the void and solid phases and the void–solid interface along a line, in a plane, and in a volume. Interpretation and practical use of the results are greatly facilitated when a lognormal model is adopted for the (central part of the) grain size distribution. The basic model is extended in various ways, to accommodate non-isotropy and non-spherical particles, and the case when it makes sense to count the fines – the smallest particles, with sizes less than a specified value – as part of the ‘effective void phase’. In the context of general multi-scale modeling of a body of granular soil, in which spatial variation occurs on multiple (larger) scales, the focus herein is on quantifying the smallest scale of fluctuation (of the component representing the discrete heterogeneity on the microscale) and on linking the multi-scale (locally averaged) stochastic continuum to the underlying particulate random medium.