Linking micro grainsize polydispersity to macro porosity

In this work we propose a micro to macro compressibility model to predict the deformation of soils with crushable grains subjected to one-dimensional compression loading. The grain size distribution of the media is described by a new index I_G defining the degree of polydispersity. I_G is linked to the evolution of the irreversible component of the deformation, while the reversible part is defined through the poroelasticity framework. The model is then applied to experimental data on monodisperse and polydisperse sand samples. Finally, this newly proposed compressibility model is coupled with an existing heterarchical multi-scale model that is able to represent how the grain size distribution evolves as a function of stress due to particle scale micromechanics. This combined heterarchical-compressibility model is shown to capture reasonably well the complex simultaneous interactions between the way the porosity, stress, and grain size distribution evolve for both initially monodisperse and polydisperse sands.