The systematic packing of prolate spheroids with reference to concentration and dilatancy

Abstract

The use of the sphere as the ideal sedimentary particle is criticised and the prolate spheroid (ellipsoid of revolution) is proposed as a more realistic alternative. Equal prolate spheroids identically oriented in space can be packed in six ways analogous to the six packings of equal spheres. The volume concentration of spheroids in systematic packing is identical with the concentration of spheres in the equivalent packing, except in cases of "cubic" packing in which concentration is a function of spheroid orientation and axial ratio. The dilatation angle of assemblages of prolate spheroids is a function of type and orientation of packing and of spheroid orientation relative to the direction of displacement. The maximum angle of initial yield of packings of spheroids is also dependent on type and orientation of packing and on spheroid orientation. The implications of these findings for the steepness and stability of slopes formed on loose granular materials are discussed.