The Theoretical Packing Density Model (TPDM): A versatile model for estimating the minimum void ratio of binary soil mixtures.

Abstract

Understanding the behavior of sand-fines mixtures and assessing their shear strength or permeability require knowledge of the influence of fine particles content on the minimum void ratio. The latter is often evaluated using empirical methods or models using parameters without physical significance. Validated for both ordered and disordered packings and for concrete mixtures, the Theoretical Packing Density Model (TPDM) is tested for predicting the minimum void ratio on binary sand-fines mixtures, whatever the fines content. It requires only two parameters: the critical cavity size ratio x0 from which the loosening effect occurs and the compaction index K describing the packing efficiency. Previously collected data from 30 binary soil mixtures including river, lake, mountain and crushed sands representing 285 individual specimens for which minimum void ratios are available, were used. The coefficient of determination provided by the TPDM is equal to 0.968 on average, and greater than 0.99 for 30% of the mixtures. Thanks to the compaction index K, the mathematical model is therefore capable to capture the non-linear behavior of the void ratio variation with respect to the solid volume fraction of fine particles. Finally, a method is proposed to approximate the value of the critical cavity size ratio x0 to be used as a function of the combination of the shapes of coarse and fine particles.