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The postulate of the existence of a jamming phase diagram (Liu and Nagel,Nature 396, 21 EP (1998aa)) provides a theoretical basis for the classificationof a wide range of amorphous solids (colloidal, molecular and emulsion glasses,colloidal and polymer gels, foams and granular matter) on the basis of whetherthese materials are in the jammed or unjammed state. Whilst such simpleclassification is appealing, it fails to capture that the criterion of rigidityof such amorphous solids may be defined with respect to a particulardeformation orientation or mode (i.e. shear, extrusion, consolidation). Weconsider this problem via the consolidation of strong colloidal gels, and findthat the critical transitions during the consolidation of a strong colloidalgel (as indicated by maxima and minima in the relative normal stressdifference) correspond directly to directed, frictional and non-frictionalrigidity percolation. These results indicate a hierarchy of directed, jammedstates during consolidation of such amorphous solids, and a direct link betweenparticle-scale interactions and macroscopic collective behaviour of thesesystems driven far from equilibrium

Hierarchical Jamming in Frictional Particle Assemblies