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Minimum void ratio or maximum packing density is an important soil property in geotechnical engineering. It apply to volume change tendency control, fluid conductivity control and particles movement.

Previous researchers have attempted to predict maximum packing density by empirical/graphic method, rock correction method, alpha method. Based on the concepts of F. de Larrard in concrete mixture research, we have developed a mathematic model that can predict the minimum void ratio for soils with a wide range of particle size.

Probability density function-lognormal distribution was tested and used to provide a reasonable representation for soils with a range of grain-size distribution. We incorporate the lognormal distribution in the mathematical model, and predict the minimum void ratio for various types of soil gradations. The validity of the model is evaluated.

The evaluation of the model is also performed on several sets of data in the literature, which include binary packing system of steel balls, ternary packing system of spheres, mixtures of round and crushed aggregates, and soils containing gravelly sand with silt. Comparison of the results will be discussed.