Grain-Size Distribution for Smallest Possible Void Ratio

In an earlier paper, the writer derived theoretical equations for void ratio as a function of grain-size distribution. Here, the equations are used to find the grain-size distributions that give the smallest possible void ratio for highly densified, cohesionless soils and similar materials that have different ratios, x₁₀₀ /x₀, for their largest and smallest grain sizes. Both numerical and analytical methods are used. Depending on the value of x₁₀₀ /x₀, materials that consist of two or three grain-size fractions with grading gaps between them have the smallest void ratios. Within the fine and coarse fractions, the grain sizes need to be as uniform as possible. The required grading of the medium fraction depends on the characteristics of the fine and coarse fractions.