An energetic state functional for saturated granular systems: Static enthalpy equilibrium as a criterion for stability and liquefaction

This work introduces an explicit mechanical enthalpy functional for granular systems subjected to gravity. The formulation provides a state-based description of stability in terms of porosity as a primary order parameter and decomposes the system energy into gravitational, structural, and hydraulic contributions. Stability is defined by the existence of a local minimum of the energetic functional, while instability corresponds to the disappearance of this minimum. In this sense, the formulation provides an explicit energetic criterion for the existence of a load-bearing granular state, which is typically assumed rather than formulated in classical approaches. The resulting framework, referred to as Static Enthalpy Equilibrium (SEE), separates state, external excitation, and kinetics, and establishes a physically transparent basis for describing stability and metastability in granular systems. While the formulation is illustrated for saturated granular systems, it is not restricted to geotechnical conditions and reflects a general stability condition for granular matter. This work provides the theoretical foundation for subsequent developments addressing the explicit role of structural degrees of freedom and dimensionless stability criteria in granular systems.