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We identify the fundamental factors determining the microstructural (MS)statistics of granular systems, using numerical experiments on 2D assemblies ofpolydisperse frictional discs and studying the emergent properties of quadrons(Qs), the basic structural elements of granular solids, whose statistics areuniversal-like[1]. The dependence of the structures and of the packing fractionon friction and initial state are analysed and we report the following. 1.Derivation of an analytical formula for the mean Q volume in terms of: the meancoordination number, the packing fraction and the rattlers fraction. 2.Derivation of a unique, initial-state-independent, relation between the meancoordination number and the rattler-free packing fraction. We support therelation with data for a range of different systems. 3. Collapse of the Qvolume distributions of all systems onto one curve, having an exponential tail.4. Decomposition of the Q volumes distribution into conditional distributions,each of these also collapsing onto a single curve. 5. The mean Q volumedecreases with increasing inter-granular friction coefficients, an effectprominent in high order cells. We argue that this phenomenon is due to anincreased probability of stable irregularly-shaped cells and test this by aherewith developed free cell analytical model. We conclude that, in principle,the MS characteristics are governed mainly by the packing procedure, whileeffects of friction and initial states can be scaled away. Yet, mechanicalconstraints limit slightly occurrence of small Q volumes in large cells, whichdoes depend on friction. We quantify this deviation from exact collapse forthese cells. 6. We argue that our results support the view that ensemblegranular statistical mechanics does not satisfy the uniform measure assumptionof conventional statistical mechanics.

Fundamental structural characteristics of planar granular assemblies: self-organisation and scaling away friction and initial state