  We identify the fundamental factors determining the microstructural (MS)
statistics of granular systems, using numerical experiments on 2D assemblies of
polydisperse frictional discs and studying the emergent properties of quadrons
(Qs), the basic structural elements of granular solids, whose statistics are
universal-like[1]. The dependence of the structures and of the packing fraction
on 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 mean
coordination number, the packing fraction and the rattlers fraction. 2.
Derivation of a unique, initial-state-independent, relation between the mean
coordination number and the rattler-free packing fraction. We support the
relation with data for a range of different systems. 3. Collapse of the Q
volume 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 volume
decreases with increasing inter-granular friction coefficients, an effect
prominent in high order cells. We argue that this phenomenon is due to an
increased probability of stable irregularly-shaped cells and test this by a
herewith developed free cell analytical model. We conclude that, in principle,
the MS characteristics are governed mainly by the packing procedure, while
effects of friction and initial states can be scaled away. Yet, mechanical
constraints limit slightly occurrence of small Q volumes in large cells, which
does depend on friction. We quantify this deviation from exact collapse for
these cells. 6. We argue that our results support the view that ensemble
granular statistical mechanics does not satisfy the uniform measure assumption
of conventional statistical mechanics.
