Hydrostatic Invariance of Structural Closure: Can Water at Rest Open a Dry-Formed Granular Assembly?

This working paper investigates whether water at rest can open an already stable granular structure. The term Structural Closure denotes a persistent, boundary-connected particle arrangement in which the contact geometry provides no accessible gravity-driven route out of the state. The particles are supported by compressive contacts, and any finite escape route encounters a positive energy barrier. The central question is: Can complete hydrostatic saturation, acting by itself, open such an existing dry-formed structure? Starting from the hydrostatic pressure field, the resultant force and moment acting on each particle are derived. For rigid, homogeneous particles made from the same material and denser than water, the combined gravitational and hydrostatic action is a common positive scalar multiple of the dry gravitational action. Water at rest reduces the effective loading but introduces neither a new force direction nor a new rotational action. The accessible particle motions, their energetic classification and the existence of compressive equilibrium therefore remain unchanged. The result does not assume that the physical saturation process leaves the initially dry arrangement undisturbed. Transient pressure gradients, capillarity, trapped gas, deformation and particle rearrangement during saturation are outside the analysis. The theorem compares dry and hydrostatic actions only at the same fixed particle configuration after such transient effects have ceased. Within these assumptions, hydrostatic saturation changes the mechanical scale of an existing Structural Closure but cannot, by itself, open it. No critical absolute pressure or water depth arises.