Composite materials technology is gradually accepted as a basis for studying the behaviour of concrete. To that end, finite element methods (FEM) are employed on composite section images. A random generator-based (RG) system is conventionally used to simulate a particulate structure of spherical grains. Neither does this allow generation of the dense-random structure of aggregate grains in concrete on macro-level (with a volume fraction of about 0.75), nor of the meso-structure of binder particles between the aggregate particles at lower water to cement ratios. Particularly, the Interfacial Transition Zone (ITZ) between bulk paste and the aggregate particles is of paramount importance for strength and durability of the material. The paper presents an analytical method relating major characteristics of the spatial structure in a randomly generated spherical particle mixture to relevant features of this structure, such as the areal fraction and the grain section size distribution function, displayed in a randomly selected cross-section. The presented example concerns a Fuller mixture, but the solution is also available for arbitrary sieve curves. In doing so, the section image for FEM application of the material can directly be derived from design data such as the sieve curve and the volume fraction of the aggregate. Studies of structure-insensitive to moderately structure-sensitive properties, depending on material composition, can be performed in this way. For structure-sensitive properties, like debonding and crack initiation, the mutual arrangement of particles (configuration) should be 'realistically' simulated. For that purpose, SPACE is introduced. It is based on a dynamic mixing of grains (reflecting the production process) of which the volume density is gradually increased to the required level. The paper shows the dramatic differences in geometrical statistical properties of particulate structures simulated by the classical RG system and by SPACE.