Pore shape evolution by solution transfer: thermodynamics and mechanics

Despite strong field and laboratory evidence of stress-controlled solution transfer, the driving forces and transport mechanisms involved are not yet well understood. To clarify the problem, we investigate the deformation of a circular pore under biaxial constant compression and filled with a fluid under pressure. It is shown that in the isotropic loading configuration, an equilibrium chemical potential, as first introduced by Gibbs, can be defined and well calculated, provided that surface and elastic energies are taken into account. When assuming the system to be at equilibrium, it is still possible to define a chemical potential for the anisotropic loading configuration although its exact calculation is no longer possible. But the chemical potential does not allow the determination of the equilibrium shape of a hole under stresses since its derivation assumes that this shape has been attained. Thus, when considering the long-term evolution of a hole which is not initially at equilibrium, another approach has to be used. We develop a theoretical treatment similar to Griffith's crack treatment involving both thermodynamics and mechanics. It allows one to predict the evolution of the pore shape by solution transfer provided that the concentration of solid in solution remains constant in the long term and the circular hole changes into an ellipse perpendicular to the applied vertical stress. The energy of the system (solid + fluid + loading device) is computed iteratively by incrementally increasing the semi-major axis of the ellipse. Equilibrium is achieved when this energy goes through a minimum. The model is then applied to the Earth's crust and leads to some predictions of the porosity structure evolution.