Evaluation of particle packing models by comparing with published test results

The existing particle packing density models each with two or more parameters accounting for certain particle interactions(the loosening effect parameter,wall effect parameter,wedging effect parameter,and compaction index,denoted by a,b,c,and K,respectively) may be classified into the 2-parameter model(with a and b incorporated),the compressible model(with a,b,and K incorporated),and the 3-parameter model(with a,b,and c incorporated).This paper evaluates these models by comparing their respective packing density predictions with the test results published in the literature.It was found that their accuracy varies with both the size ratio and volumetric fractions of the binary mix.In general,when the size ratio is larger than 0.65,all the packing models are sufficiently accurate.However,when the size ratio is smaller than 0.65,some of them become inaccurate and the errors tend to be larger at around the volumetric fractions giving maximum packing density.Relatively,the 3-parameter model is the most accurate and widely applicable.