Post-collapse densification as an energy-conditioned state evolution in saturated granular systems

This article presents a physically consistent interpretation of post-collapse densification in saturated granular systems, based on a state-based and energy-conditioned framework. Post-collapse densification is treated as the final stage of a continuous state evolution following spontaneous liquefaction and geometric readjustment, rather than as renewed failure or instability. The analysis is grounded in the Zander-12 column experiment, which serves as a canonical reference system. The experimental configuration deliberately suppresses horizontal deformation and lateral spreading, thereby isolating the interior behaviour of a liquefied granular domain. This allows the intrinsic physics of post-collapse densification to be examined independently of boundary-controlled or geometry-driven effects. The results demonstrate that post-collapse densification proceeds through a lamella-controlled redistribution of solid and water volumes under strict volume conservation. The underlying mechanism remains invariant over repeated excitation events, while the densification increment per excitation decreases asymptotically. No qualitative change in behaviour is observed when approaching conditions commonly associated with the classical liquefaction boundary. Within the Static Enthalpy Equilibrium (SEE) framework, post-collapse densification is interpreted as a state-controlled relaxation process, characterized by a progressive reduction of residual structural enthalpy. The system evolves toward an energy-conditioned asymptotic end porosity , which depends on the magnitude of the applied excitation energy. This end state represents a local minimum in the system’s state landscape and must be distinguished from the densest physically admissible packing, which constitutes an absolute geometric limit that remains inaccessible under finite excitation energy. The study clarifies why repeated excitations often lead to progressively smaller settlements without renewed large-scale deformation, and why post-collapse densification may become weak or hardly detectable despite ongoing microstructural rearrangement. While field geometries may superimpose additional boundary effects, the mechanism identified here represents a fundamental state-controlled process expected to operate within the interior of liquefied granular domains.