Disordered granular packs present many challenges over regular structures in description, analysis and modelling. Within the granular statistical mechanics, which aims to compute bulk properties from details of the local structure, the quadron description was defined over a decade ago. This quantitative characterisation of disordered systems enumerates the structural degrees of freedom, by dividing the system into tessellating volume elements, quadrons, and assigning each a quantitative structure tensor computed from its shape. Presented in this work is a theoretical derivation of an equipartition principle of the volume, which is the analogue of the well known 3kT/2 in thermal physics. This computation is included in full, for two-dimensional systems, using the quadron description. Following this, quadron tensors and statistics in three dimensional disordered structures are computed and analysed for the first time. A new computer program to achieve this was developed, requiring a new class of solution for cell/pore identification, a custom 3D rendering engine, and several extensions to the quadron description as originally defined. The program was successful in analysing structures from simulations, experimental colloidal suspensions and granular systems of a few thousand grains. By a subsystem-based parallelisation method, much larger data-sets were successfully analysed, including an X-ray tomography experiment with 60,000 non-spherical grains. The quadron statistics of a triaxial shear experiment were computed at multiple stages, and the chirality, a pseudo-vector computed from the structure tensor which measures the deviation from orthogonality of the volume element boundary, develops an anisotropy during the formation of a shear band. While the software performed very well on dense granular packs, its performance in less dense systems or regions, like a shear band, was both slower and less reliable. This was traced to the increased ambiguity in cell structure as the density decreases, and is something that future analysis could improve.
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