Evaluation of three packing density models on reference particle-size distributions

Abstract

Multi-sized mixtures are frequently encountered in soils, industry and construction. In many cases, the particle-size distribution (PSD) must be optimized to achieve a certain packing density, the estimation of which must be as precise as possible. For this purpose, three packing density models are evaluated from published data on PSDs of spheres, angular flint, crushed aggregates: the Compressible Packing Model (CPM), the 3-parameter Particle Packing Model (3PPM), the Theoretical Packing Density Model (TPDM). The PSDs exploited are complementary: power-laws, truncated power-laws, uniform distributions by volume and fractal models. They then make it possible to focus the estimates of packing density on reference PSDs: the century-old power-law of Fuller & Thompson (FT) and the Caquot’s distribution for concrete, the “well-graded” size distribution in soil classification. The conclusions are as follows. The 3PPM underestimates packing densities due to an overvaluation of the geometric interactions. The CPM overestimates packing densities due to an underestimation of the loosening effect in a certain range of size ratios. The TPDM provides the most homogeneous estimates with prediction error values almost all below 2%. Due to its efficiency, the TPDM is used on model materials whose granular extent varies between 1 and 10,000 to determine the preferred domain of each of the reference PSDs.

Graphic abstract