Terrain readjustment due to spontaneous liquefaction in saturated granular deposits – a two-dimensional end-state model (SEE)

This work presents a state-based end-state formulation for terrain readjustment after liquefaction in saturated granular deposits. The analysis focuses on the geometrically admissible configurations that establish once mobilization has occurred, derived from energy minimization under strict mass conservation. The formulation is deliberately independent of triggering mechanisms, temporal evolution, and constitutive stress–strain descriptions. Admissible configurations are shown to form a sequence of metastable end states, characterized by local geometric equilibration. A configuration of constant elevation represents the asymptotic geometric attractor of repeated admissible states rather than the immediate outcome of a single liquefaction event. A representative closed-domain example illustrates that the dominant geometric adjustment occurs during the first mobilization, while subsequent admissible states involve only minor internal readjustment that may be difficult to detect.The closed-domain formulation presented here serves as a geometric reference case for future extensions to systems with open boundaries or evolving constraints.