A 3-parameter particle packing model for spherical and non-spherical particles

Abstract

In many fields of industries, it has been found that the properties of granular materials are intimately related to their packing densities. To find the particle size distribution for optimum packing density rendering the best performance of granular materials, it is useful to have a particle packing model which can accurately predict the packing density of granular materials. Nevertheless, the development of particle packing model is difficult and complex as there are many factors affecting packing density including particle shape, packing method and formation of agglomerates between cohesive fine particles.

Even for binary mixes of particles, the existing 2-parameter model which takes into account the loosening effect and the wall effect and assumes a linear relationship between specific volume (reciprocal of packing density) and volumetric fractions of particles, does not give satisfactory prediction. Through comprehensive experimental study, the author has found that the deviations from experimental results are caused by the wedging effect of the fine particles situating at the gaps between the coarse particles producing extra voids. The newly identified wedging effect was incorporated into the 3-parameter model, in which the specific volume is no longer a linear function of the volumetric fractions. This thesis presents the further development of the 3-parameter model, which is extended to ternary mixes and multi-component mixes of spherical and non-spherical particles with various factors affecting packing density taken into account.

In extending the 3-parameter model to ternary mixes and multi-component mixes of particles, an approach was adopted so that the final packing density of the mixture consisting of several size classes was taken as the minimum of those determined from a set of equations, each corresponding to one dominant size class. The extended model was verified using the experimental results of spherical particles obtained from this study and cylindrical particles obtained from the literature. The accuracy of the model was also compared to other existing models for multi-component mixes, such as the 2-parameter model and the compressible packing model.

For more general applications to angular aggregate particles, the 3-parameter model was modified by a number of adjustments which include the re-derivation of the interaction functions of the three parameters accounting for the loosening, wall and wedging effects under both uncompacted and compacted packing conditions. However, it was demonstrated that without the consideration of the formation of agglomerates between cohesive fine particles, which would produce extra voids known as the agglomeration effect, would result in interaction functions giving unreasonable interpretation of the various interaction effects. Consequently, the 3-parameter model was also modified to account for the agglomeration effect. Finally, for application in concrete industry, the 3-parameter model was also modified for continuous grading of aggregate particles, which would be helpful in determining the optimum particle size distribution of aggregate particles so as to further improve the performance of concrete.

Overall, the modified and extended 3-parameter model was verified to provide accurate prediction and would be a useful tool for optimizing the particle size distribution in various fields of industries.