Differentiated structures arising from mechano-chemical feedback in stressed rocks

Abstract

We review some of our mathematical modeling efforts toward describing the interaction between a deforming rock and its contained fluid. Specifically, we advocate the concept of self-organization as a means of understanding the evolution of patterned structures observed in rocks ranging from diagenetic to metamorphic conditions. These arise from feedbacks resulting from the coupling of mechanical forces with chemical reactions and transport, due to the dependence of mineral free energy on surrounding rock texture. The same formalism in different limiting or initial conditions captures much of the behavior observed with such deformation-related structures as stylolites, intergranular pressure solution, spaced cleavage, metamorphic layering, and mineralized segregations arising from the force exerted by crystal growth. The equations predict the likelihood of any tendency toward differentiation, and show how chemical factors impose strong constraints on the deformational response of a rock.