Maximum dry density for a continuous grain size distribution

A theoretical expression for the optimum packing density of a continuous particle size distribution has been derived. The constituent particles are assumed to be nondeformable spheres, devoid of bonding or cohesive properties. The calculation extended the results of optimum packing for binary, ternary, quartenary, and quinary systems to higher orders and applied them to a continuous linear grain size distribution. It is found that the theoretical upper limit in packing density, η, is dependent of mean size but well described by a piecewise linear function in the inverse of the packing density as a function of the slope s of the distribution. Laboratory measurements of maximum packing density for about eighty five soil samples have been fitted to the theoretically predicted functional form. A nomograph has been drawn based on the fitted values which allows the estimation of the maximum dry density of granular soil sample with an accuracy of 3.5% if the slope of its grain size distribution is known. The effect of the fine contents (percent passing No. 200 sieve) of the soils distribution has been included.