Use of Machine Learning for unraveling hidden correlations between Particle Size Distributions and the Mechanical Behavior of Granular Materials

Among the intrinsic properties of a sand, the surface friction, the compressibility and the strength of individual grains, the particle shape and particle size distributions are known to play a crucial role in its macroscopic properties [1, 2, 3, 4]. Relative density and confining pressure are the most influent state variables for dry granular soils [5] and govern the mechanical behavior of the material to a large extent [6, 7, 8]. The relationship between the particle size distribution, PSD, and the mechanical behavior is not yet fully understood. On one hand, the effects of variations in the PSD are not independent from those produced by variations of other intrinsic properties or state parameters. For example, the state parameter ψ, proposed within the theoretical framework of the critical state of sands [5], helps to distinguish between the contractive or dilatant behavior exhibited by a sand upon triaxial compression. However the critical state line, and hence the value of ψ associated to given void ratio e, changes with the PSD [9]. As another example, there is a complex interplay between size and shape polydispersity, as shown by numerical modeling [10]. On the other hand, linking single quantities (maximum and minimum dry density, critical state void ratio, macroscopic friction angle, stiffness, etc.) to a PSD is not immediate, since the latter is a highly variable curve that is many times long-tailed and/or multi-modal. Descriptors derived from the PSD are not enough to anticipate macroscopic (void ratio, stiffness, friction angle) or microscopic features (average coordination number, fraction of non-contributing particles, etc.) obtained after a given process.